@inproceedings{17126,
  abstract     = {Functional encryption (FE) is a primitive where the holder of a master secret key can control which functions a user can evaluate on encrypted data. It is a powerful primitive that even implies indistinguishability obfuscation (iO), given sufficiently compact ciphertexts (Ananth-Jain, CRYPTO’15 and Bitansky-Vaikuntanathan, FOCS’15). However, despite being extensively studied, there are FE schemes, such as function-hiding inner-product FE (Bishop-Jain-Kowalczyk, AC’15, Abdalla-Catalano-Fiore-Gay-Ursu, CRYPTO’18) and compact quadratic FE (Baltico-Catalano-Fiore-Gay, Lin, CRYPTO’17), that can be only realized using pairings. This raises the question if there are some mathematical barriers that hinder us from realizing these FE schemes from other assumptions.

In this paper, we study the difficulty of constructing lattice-based compact FE. We generalize the impossibility results of Ünal (EC’20) for lattice-based function-hiding FE, and extend it to the case of compact FE. Concretely, we prove lower bounds for lattice-based compact FE schemes which meet some (natural) algebraic restrictions at encryption and decryption, and have ciphertexts of linear size and secret keys of minimal degree. We see our results as important indications of why it is hard to construct lattice-based FE schemes for new functionalities, and which mathematical barriers have to be overcome.},
  author       = {Tairi, Erkan and Ünal, Akin},
  booktitle    = {Advances in Cryptology – EUROCRYPT 2024},
  isbn         = {9783031587221},
  issn         = {1611-3349},
  location     = {Zurich, Switzerland},
  pages        = {249--279},
  publisher    = {Springer Nature},
  title        = {{Lower bounds for lattice-based compact functional encryption}},
  doi          = {10.1007/978-3-031-58723-8_9},
  volume       = {14652},
  year         = {2024},
}

@inproceedings{18755,
  abstract     = {A universalthresholdizer (UT), constructed from a threshold fully homomorphic encryption by Boneh et. al , Crypto 2018, is a general framework for universally thresholdizing many cryptographic schemes. However, their framework is insufficient to construct strongly secure threshold schemes, such as threshold signatures and threshold public-key encryption, etc.

In this paper, we strengthen the security definition for a universal thresholdizer and propose a scheme which satisfies our stronger security notion. Our UT scheme is an improvement of Boneh et. al ’s construction at the level of threshold fully homomorphic encryption using a key homomorphic pseudorandom function. We apply our strongly secure UT scheme to construct strongly secure threshold signatures and threshold public-key encryption.},
  author       = {Ebrahimi, Ehsan and Yadav, Anshu},
  booktitle    = {30th International Conference on the Theory and Application of Cryptology and Information Security},
  isbn         = {9789819608904},
  issn         = {1611-3349},
  location     = {Kolkata, India},
  pages        = {207--239},
  publisher    = {Springer Nature},
  title        = {{Strongly secure universal thresholdizer}},
  doi          = {10.1007/978-981-96-0891-1_7},
  volume       = {15486},
  year         = {2024},
}

@inproceedings{18974,
  abstract     = {Reinforcement Learning (RL) from temporal logical specifications is a fundamental problem in sequential decision making. One of the basic and core such specification is the reachability specification that requires a target set to be eventually visited. Despite strong empirical results for RL from such specifications, the theoretical guarantees are bleak, including the impossibility of Probably Approximately Correct (PAC) guarantee for reachability specifications. Given the impossibility result, in this work we consider the problem of RL from reachability specifications along with the information of expected conditional distance (ECD). We present (a) lower bound results which establish the necessity of ECD information for PAC guarantees and (b) an algorithm that establishes PAC-guarantees given the ECD information. To the best of our knowledge, this is the first RL from reachability specifications that does not make any assumptions on the underlying environment to learn policies.},
  author       = {Svoboda, Jakub and Bansal, Suguman and Chatterjee, Krishnendu},
  booktitle    = {41st International Conference on Machine Learning},
  location     = {Vienna, Austria},
  pages        = {47331--47344},
  publisher    = {ML Research Press},
  title        = {{Reinforcement learning from reachability specifications: PAC guarantees with expected conditional distance}},
  volume       = {235},
  year         = {2024},
}

@phdthesis{18088,
  abstract     = {Instant messaging applications like Whatsapp, Signal or Telegram have become ubiquitous in today's society.
Many of them provide not only end-to-end encryption, but also security guarantees even when the key material gets compromised.
These are achieved through frequent key update performed by users.
In particular, the compromise of a group key should preserve confidentiality of previously exchanged messages (forward secrecy), and a subsequent key update will ensure security for future ones (post-compromise security).
Though great protocols for one-on-one communication have been known for some time, the design of ones that scale efficiently for larger groups while achieving akin security guarantees is a hard problem.
A great deal of research has been aimed at this topic, much of it under the umbrella of the Messaging Layer Security (MLS) working group at the IETF. 
Started in 2018, this joint effort by academics and industry culminated in 2023 with the publication of the first standard for secure group messaging [IETF, RFC9420].

At the core of secure group messaging is a cryptographic primitive termed Continuous Group Key Agreement, or CGKA [Alwen et al. 2021], that essentially allows a changing group of users to agree on a common key with the added functionality security against compromises is achieved by users asynchronously issuing a key update. In this thesis we contribute to the understanding of CGKA across different angles.
First, we present a new technique to effect dynamic operations in groups, i.e., add or remove members, that can be more efficient that the one employed by MLS in certain settings.
Considering the setting of users belonging to multiple overlapping groups, we then show lowerbounds on the communication cost of constructions that leverage said overlap, at the same time showing protocols that are asymptotically optimal and efficient for practical settings, respectively. Along the way, we show that the communication cost of key updates in MLS is average-cost optimal.
An important feature in CGKA protocols, particularly for big groups, is the possibility of executing several group operations concurrently. While later versions of MLS support this, they do at the cost of worsening the communication efficiency of future group operations.
In this thesis we introduce two new protocols that permit concurrency without any negative effect on efficiency. Our protocols circumvent previously existing lower bounds by satisfying a new notion of post-compromise security that only asks for security to be re-established after a certain number of key updates have taken place. While this can be slower than MLS in terms of rounds of communication, we show that it leads to more efficient overall communication. 
Additionally, we introduce a new technique that allows group members to decrease the information they need to store and download, which makes one of our protocols enjoy much lower download cost than any other existing CGKA constructions. },
  author       = {Pascual Perez, Guillermo},
  issn         = {2663-337X},
  pages        = {239},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{On the efficiency and security of secure group messaging}},
  doi          = {10.15479/at:ista:18088},
  year         = {2024},
}

@inproceedings{18086,
  abstract     = {Abstract. Continuous group key agreement (CGKA) allows a group of
users to maintain a continuously updated shared key in an asynchronous
setting where parties only come online sporadically and their messages
are relayed by an untrusted server. CGKA captures the basic primitive
underlying group messaging schemes.
Current solutions including TreeKEM (“Messaging Layer Security”
(MLS) IETF RFC 9420) cannot handle concurrent requests while retaining low communication complexity. The exception being CoCoA, which
is concurrent while having extremely low communication complexity (in
groups of size n and for m concurrent updates the communication per
user is log(n), i.e., independent of m). The main downside of CoCoA
is that in groups of size n, users might have to do up to log(n) update
requests to the server to ensure their (potentially corrupted) key material has been refreshed.
In this work we present a “fast healing” concurrent CGKA protocol,
named DeCAF, where users will heal after at most log(t) requests, with
t being the number of corrupted users. While also suitable for the standard central-server setting, our protocol is particularly interesting for
realizing decentralized group messaging, where protocol messages (add,
remove, update) are being posted on some append-only data structure
rather than sent to a server. In this setting, concurrency is crucial once
the rate of requests exceeds, say, the rate at which new blocks are added
to a blockchain.
In the central-server setting, CoCoA (the only alternative with concurrency, sub-linear communication and basic post-compromise security)
enjoys much lower download communication. However, in the decentralized setting – where there is no server which can craft specific messages
for different users to reduce their download communication – our protocol
significantly outperforms CoCoA. DeCAF heals in fewer epochs (log(t)
vs. log(n)) while incurring a similar per epoch per user communication
cost.},
  author       = {Alwen, Joel F and Auerbach, Benedikt and Cueto Noval, Miguel and Klein, Karen and Pascual Perez, Guillermo and Pietrzak, Krzysztof Z},
  booktitle    = {Security and Cryptography for Networks: 14th International Conference},
  editor       = {Galdi, Clemente and Phan, Duong Hieu},
  isbn         = {9783031710728},
  issn         = {1611-3349},
  location     = {Amalfi, Italy},
  pages        = {294–313},
  publisher    = {Springer Nature},
  title        = {{DeCAF: Decentralizable CGKA with fast healing}},
  doi          = {10.1007/978-3-031-71073-5_14},
  volume       = {14974},
  year         = {2024},
}

@article{18961,
  abstract     = {Automated contact tracing (ACT) emerged as a promising measure to curb the spread of Covid-19. Users enable ACT on their smartphones to automatically record contacts with other users. If a user tests positive for the disease, they report their diagnosis to alert their contacts.
Designing effective ACT protocols is challenging since they need to be efficient and secure while also ensuring users' privacy. As ACT protocols necessarily leak some information by design, defining privacy is difficult. For example, a user cannot deny having met another user. Ideally, however, the user can plausibly deny everything else, in particular, when they met. We call this privacy property contact-time deniability.
While some early works discussed contact-time deniability informally, it has received little attention since then. We investigate deniability from a rigorous, theoretical point of view and arrive at the following impossibility result:
A decentralized protocol with unidirectional communication cannot be contact-time deniable and replay-secure. This holds even if malicious users treat smartphones as black-boxes.
 Unidirectional protocols are usually very efficient and many proposals are unidirectional, e.g., the widely-deployed Google-Apple Exposure Notifications. So the impossibility result considerably constrains the design space of efficient, secure, and private ACT protocols. However, it can also be used as a guide; we discuss several possibilities to achieve contact-time deniability in practice.},
  author       = {Günther, Christoph Ullrich and Pietrzak, Krzysztof Z},
  issn         = {2299-0984},
  journal      = {Proceedings on Privacy Enhancing Technologies},
  location     = {Bristol, UK/Virtual},
  number       = {4},
  pages        = {636--648},
  publisher    = {Privacy Enhancing Technologies Symposium Advisory Board},
  title        = {{Deniability in automated contact tracing: Impossibilities and possibilities}},
  doi          = {10.56553/popets-2024-0134},
  volume       = {2024},
  year         = {2024},
}

@article{18554,
  abstract     = {We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure.},
  author       = {Erdös, László and Riabov, Volodymyr},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {12},
  publisher    = {Springer Nature},
  title        = {{Eigenstate Thermalization Hypothesis for Wigner-type matrices}},
  doi          = {10.1007/s00220-024-05143-y},
  volume       = {405},
  year         = {2024},
}

@article{13975,
  abstract     = {We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An
 is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln  converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure.},
  author       = {Campbell, Andrew J and O’Rourke, Sean},
  issn         = {1572-9230},
  journal      = {Journal of Theoretical Probability},
  pages        = {933--973},
  publisher    = {Springer Nature},
  title        = {{Spectrum of Lévy–Khintchine random laplacian matrices}},
  doi          = {10.1007/s10959-023-01275-4},
  volume       = {37},
  year         = {2024},
}

@article{17281,
  abstract     = {We extend the free convolution of Brown measures of R-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions.},
  author       = {Campbell, Andrew J and O'Rourke, Sean and Renfrew, David T},
  issn         = {1687-0247},
  journal      = {International Mathematics Research Notices},
  number       = {13},
  pages        = {10189--10218},
  publisher    = {Oxford University Press},
  title        = {{The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation}},
  doi          = {10.1093/imrn/rnae062},
  volume       = {2024},
  year         = {2024},
}

@article{14408,
  abstract     = {We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0
, to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator.},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1432-2064},
  journal      = {Probability Theory and Related Fields},
  pages        = {1131--1182},
  publisher    = {Springer Nature},
  title        = {{Mesoscopic central limit theorem for non-Hermitian random matrices}},
  doi          = {10.1007/s00440-023-01229-1},
  volume       = {188},
  year         = {2024},
}

@article{17375,
  abstract     = {We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion.},
  author       = {Cipolloni, Giorgio and Erdös, László and Xu, Yuanyuan},
  issn         = {0022-2488},
  journal      = {Journal of Mathematical Physics},
  number       = {6},
  publisher    = {AIP Publishing},
  title        = {{Precise asymptotics for the spectral radius of a large random matrix}},
  doi          = {10.1063/5.0209705},
  volume       = {65},
  year         = {2024},
}

@article{15025,
  abstract     = {We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble.},
  author       = {Erdös, László and McKenna, Benjamin},
  issn         = {1050-5164},
  journal      = {Annals of Applied Probability},
  number       = {1B},
  pages        = {1623--1662},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Extremal statistics of quadratic forms of GOE/GUE eigenvectors}},
  doi          = {10.1214/23-AAP2000},
  volume       = {34},
  year         = {2024},
}

@phdthesis{17164,
  abstract     = {This thesis is structured into two parts. In the first part, we consider the random
variable X := Tr(f1(W)A1 . . . fk(W)Ak) where W is an N × N Hermitian Wigner matrix, k ∈ N, and we choose (possibly N-dependent) regular functions f1, . . . , fk as well as
bounded deterministic matrices A1, . . . , Ak. In this context, we prove a functional central
limit theorem on macroscopic and mesoscopic scales, showing that the fluctuations of X
around its expectation are Gaussian and that the limiting covariance structure is given
by a deterministic recursion. We further give explicit error bounds in terms of the scaling
of f1, . . . , fk and the number of traceless matrices among A1, . . . , Ak, thus extending
the results of Cipolloni, Erdős and Schröder [40] to products of arbitrary length k ≥ 2.
Analyzing the underlying combinatorics leads to a non-recursive formula for the variance
of X as well as the covariance of X and Y := Tr(fk+1(W)Ak+1 . . . fk+ℓ(W)Ak+ℓ) of similar
build. When restricted to polynomials, these formulas reproduce recent results of Male,
Mingo, Peché, and Speicher [107], showing that the underlying combinatorics of noncrossing partitions and annular non-crossing permutations continue to stay valid beyond
the setting of second-order free probability theory. As an application, we consider the
fluctuation of Tr(eitW A1e
−itW A2)/N around its thermal value Tr(A1) Tr(A2)/N2 when t
is large and give an explicit formula for the variance.
The second part of the thesis collects three smaller projects focusing on different random
matrix models. In the first project, we show that a class of weakly perturbed Hamiltonians
of the form Hλ = H0 + λW, where W is a Wigner matrix, exhibits prethermalization.
That is, the time evolution generated by Hλ relaxes to its ultimate thermal state via an
intermediate prethermal state with a lifetime of order λ
−2
. As the main result, we obtain
a general relaxation formula, expressing the perturbed dynamics via the unperturbed
dynamics and the ultimate thermal state. The proof relies on a two-resolvent global law
for the deformed Wigner matrix Hλ.
The second project focuses on correlated random matrices, more precisely on a correlated N × N Hermitian random matrix with a polynomially decaying metric correlation
structure. A trivial a priori bound shows that the operator norm of this model is stochastically dominated by √
N. However, by calculating the trace of the moments of the matrix
and using the summable decay of the cumulants, the norm estimate can be improved to a
bound of order one.
In the third project, we consider a multiplicative perturbation of the form UA(t) where U
is a unitary random matrix and A = diag(t, 1, ..., 1). This so-called UA model was
first introduced by Fyodorov [73] for its applications in scattering theory. We give a
general description of the eigenvalue trajectories obtained by varying the parameter t and
introduce a flow of deterministic domains that separates the outlier resulting from the
rank-one perturbation from the typical eigenvalues for all sub-critical timescales. The
results are obtained under generic assumptions on U that hold for various unitary random
matrices, including the circular unitary ensemble (CUE) in the original formulation of
the model.},
  author       = {Reker, Jana},
  issn         = {2663-337X},
  keywords     = {Random Matrices, Spectrum, Central Limit Theorem, Resolvent, Free Probability},
  pages        = {206},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Central limit theorems for random matrices: From resolvents to free probability}},
  doi          = {10.15479/at:ista:17164},
  year         = {2024},
}

@article{17049,
  abstract     = {We consider large non-Hermitian NxN matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance 1/N completely thermalises the bulk singular vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity (QUE) with an optimal speed of convergence. In physics terms, we thus extend the Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also known as the (square of the) eigenvalue condition number measuring the sensitivity of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment beyond the explicitly computable Ginibre ensemble apart from the very recent upper bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition of general observables in random matrix theory that governs the size of products of resolvents with deterministic matrices in between.},
  author       = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha and Schröder, Dominik J},
  issn         = {1096-0783},
  journal      = {Journal of Functional Analysis},
  number       = {4},
  publisher    = {Elsevier},
  title        = {{Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices}},
  doi          = {10.1016/j.jfa.2024.110495},
  volume       = {287},
  year         = {2024},
}

@article{15378,
  abstract     = {We consider N×N non-Hermitian random matrices of the form X+A, where A is a general deterministic matrix and N−−√X consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1); both results are optimal up to the factor No(1). The latter result complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for the small singular values of X+A−z, is of independent interest.},
  author       = {Erdös, László and Ji, Hong Chang},
  issn         = {1097-0312},
  journal      = {Communications on Pure and Applied Mathematics},
  number       = {9},
  pages        = {3785--3840},
  publisher    = {Wiley},
  title        = {{Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices}},
  doi          = {10.1002/cpa.22201},
  volume       = {77},
  year         = {2024},
}

@article{18762,
  abstract     = {Consider the random variable $\mathrm{Tr}( f_1(W)A_1\dots f_k(W)A_k)$ where $W$ is an $N\times N$ Hermitian Wigner matrix, $k\in\mathbb{N}$, and choose (possibly $N$-dependent) regular functions $f_1,\dots, f_k$ as well as bounded deterministic matrices $A_1,\dots,A_k$. We give a functional central limit theorem showing that the fluctuations around the expectation are Gaussian. Moreover, we determine the limiting covariance structure and give explicit error bounds in terms of the scaling of $f_1,\dots,f_k$ and the number of traceless matrices among $A_1,\dots,A_k$, thus extending the results of [Cipolloni, Erdős, Schröder 2023] to products of arbitrary length $k\geq2$. As an application, we consider the fluctuation of $\mathrm{Tr}(\mathrm{e}^{\mathrm{i} tW}A_1\mathrm{e}^{-\mathrm{i} tW}A_2)$ around its thermal value $\mathrm{Tr}(A_1)\mathrm{Tr}(A_2)$ when $t$ is large and give an explicit formula for the variance.},
  author       = {Reker, Jana},
  issn         = {1083-6489},
  journal      = {Electronic Journal of Probability},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Multi-point functional central limit theorem for Wigner matrices}},
  doi          = {10.1214/24-EJP1247},
  volume       = {29},
  year         = {2024},
}

@article{17154,
  abstract     = {We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of Male et al. (Random Matrices Theory Appl. 11(2):2250015, 2022), showing that the underlying combinatorics of non-crossing partitions and annular non-crossing permutations continue to stay valid beyond the setting of second-order free probability theory. The formulas obtained further characterize the variance in the functional central limit theorem given in the recent companion paper (Reker in Preprint, arXiv:2204.03419, 2023). and thus allow identifying the fluctuation around the thermal value in certain thermalization problems.},
  author       = {Reker, Jana},
  issn         = {1572-9656},
  journal      = {Mathematical Physics, Analysis and Geometry},
  number       = {3},
  publisher    = {Springer Nature},
  title        = {{Fluctuation moments for regular functions of Wigner Matrices}},
  doi          = {10.1007/s11040-024-09483-y},
  volume       = {27},
  year         = {2024},
}

@article{18656,
  abstract     = {We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables 
 and 
 in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11]).},
  author       = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha},
  issn         = {1095-0753},
  journal      = {Advances in Theoretical and Mathematical Physics},
  number       = {6},
  pages        = {2025--2083},
  publisher    = {International Press of Boston},
  title        = {{Out-of-time-ordered correlators for Wigner matrices}},
  doi          = {10.4310/ATMP.241031013250},
  volume       = {28},
  year         = {2024},
}

@article{17326,
  abstract     = {Magnetic fields in the stellar interiors are key candidates to explain observed core rotation rates inside solar-like stars along their evolution. Recently, asteroseismic estimates of radial magnetic field amplitudes near the hydrogen-burning shell (H-shell) inside about 24 red giants (RGs) have been obtained by measuring frequency splittings from their power spectra. Using general Lorentz-stress (magnetic) kernels, we investigated the potential for detectability of near-surface magnetism in a 1.3 M⊙ star of supersolar metallicity as it evolves from a mid subgiant to a late subgiant into an RG. Based on these sensitivity kernels, we decompose an RG into three zones—deep core, H-shell, and near-surface. The subgiants instead required decomposition into an inner core, an outer core, and a near-surface layer. Additionally, we find that for a low-frequency g-dominated dipolar mode in the presence of a typical stable magnetic field, ∼25% of the frequency shift comes from the H-shell and the remaining from deeper layers. The ratio of the subsurface tangential field to the radial field in the H-burning shell decides if subsurface fields may be potentially detectable. For p-dominated dipole modes close to vmax, this ratio is around two orders of magnitude smaller in subgiant phases than the corresponding RG. Further, with the availability of magnetic kernels, we propose lower limits of field strengths in crucial layers in our stellar model during its evolutionary phases. The theoretical prescription outlined here provides the first formal way to devise inverse problems for stellar magnetism and can be seamlessly employed for slow rotators.},
  author       = {Bhattacharya, Shatanik and Das, Srijan B and Bugnet, Lisa Annabelle and Panda, Subrata and Hanasoge, Shravan M.},
  issn         = {1538-4357},
  journal      = {Astrophysical Journal},
  number       = {1},
  publisher    = {IOP Publishing},
  title        = {{Detectability of axisymmetric magnetic fields from the core to the surface of oscillating post-main-sequence stars}},
  doi          = {10.3847/1538-4357/ad4708},
  volume       = {970},
  year         = {2024},
}

@article{18172,
  abstract     = {Red Giant stars host solar-like oscillations which have mixed character, being sensitive to conditions both in the outer convection zone and deep within the interior. The properties of these modes are sensitive to both core rotation and magnetic fields. While asteroseismic studies of the former have been done on a large scale, studies of the latter are currently limited to tens of stars. We aim to produce the first large catalogue of both magnetic and rotational perturbations. We jointly constrain these parameters by devising an automated method for fitting the power spectra directly. We successfully apply the method to 302 low-luminosity red giants. We find a clear bimodality in core rotation rate. The primary peak is at δνrot = 0.32 μHz, and the secondary at δνrot = 0.47 μHz. Combining our results with literature values, we find that the percentage of stars rotating much more rapidly than the population average increases with evolutionary state. We measure magnetic splittings of 2σ significance in 23 stars. While the most extreme magnetic splitting values appear in stars with masses > 1.1M⊙, implying they formerly hosted a convective core, a small but statistically significant magnetic splitting is measured at lower masses. Asymmetry between the frequencies of a rotationally split multiplet has previously been used to diagnose the presence of a magnetic perturbation. We find that of the stars with a significant detection of magnetic perturbation, 43\% do not show strong asymmetry. We find no strong evidence of correlation between the rotation and magnetic parameters.},
  author       = {Hatt, Emily J. and Ong, J. M.Joel and Nielsen, Martin B. and Chaplin, William J. and Davies, Guy R. and Deheuvels, Sébastien and Ballot, Jérôme and Li, Gang and Bugnet, Lisa Annabelle},
  issn         = {1365-2966},
  journal      = {Monthly Notices of the Royal Astronomical Society},
  number       = {2},
  pages        = {1060--1076},
  publisher    = {Oxford University Press},
  title        = {{Asteroseismic signatures of core magnetism and rotation in hundreds of low-luminosity red giants}},
  doi          = {10.1093/mnras/stae2053},
  volume       = {534},
  year         = {2024},
}