@article{20591,
  abstract     = {In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions to the heat equation. For initial data in the form of log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian admits an explicit, uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant of a transport map pushing forward the standard Gaussian to a measure in this class. On the other hand, we show that assuming only fast decay of the tails of the initial datum does not suffice to guarantee uniform log-Hessian upper bounds.},
  author       = {Brigati, Giovanni and Pedrotti, Francesco},
  issn         = {1083-589X},
  journal      = {Electronic Communications in Probability},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Heat flow, log-concavity, and Lipschitz transport maps}},
  doi          = {10.1214/25-ECP717},
  volume       = {30},
  year         = {2025},
}

@article{18655,
  abstract     = {Let Qd be the d-dimensional binary hypercube. We say that P={v1,…,vk} is an increasing path of length k−1 in Qd, if for every i∈[k−1] the edge vivi+1 is obtained by switching some zero coordinate in vi to a one coordinate in vi+1.
Form a random subgraph Qdp by retaining each edge in E(Qd) independently with probability p. We show that there is a phase transition with respect to the length of a longest increasing path around p=ed. Let α be a constant and let p=αd. When α<e, then there exists a δ∈[0,1) such that whp a longest increasing path in Qdp is of length at most δd. On the other hand, when α>e, whp there is a path of length d−2 in Qdp, and in fact, whether it is of length d−2,d−1, or d depends on whether the all-zero and all-one vertices percolate or not.},
  author       = {Anastos, Michael and Diskin, Sahar and Elboim, Dor and Krivelevich, Michael},
  issn         = {1083-589X},
  journal      = {Electronic Communications in Probability},
  publisher    = {Duke University Press},
  title        = {{Climbing up a random subgraph of the hypercube}},
  doi          = {10.1214/24-ECP639},
  volume       = {29},
  year         = {2024},
}

@article{12683,
  abstract     = {We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices.},
  author       = {Dubach, Guillaume and Erdös, László},
  issn         = {1083-589X},
  journal      = {Electronic Communications in Probability},
  pages        = {1--13},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Dynamics of a rank-one perturbation of a Hermitian matrix}},
  doi          = {10.1214/23-ECP516},
  volume       = {28},
  year         = {2023},
}

@article{13145,
  abstract     = {We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.},
  author       = {Dello Schiavo, Lorenzo and Lytvynov, Eugene},
  issn         = {1083-589X},
  journal      = {Electronic Communications in Probability},
  pages        = {1--12},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{A Mecke-type characterization of the Dirichlet–Ferguson measure}},
  doi          = {10.1214/23-ECP528},
  volume       = {28},
  year         = {2023},
}