TY - CONF AB - We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices. AU - Betea, Dan AU - Bouttier, Jérémie AU - Nejjar, Peter AU - Vuletíc, Mirjana ID - 8175 T2 - Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics TI - New edge asymptotics of skew Young diagrams via free boundaries ER - TY - JOUR AB - We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently. AU - Virosztek, Daniel ID - 405 JF - Linear Algebra and Its Applications TI - Jointly convex quantum Jensen divergences VL - 576 ER - TY - JOUR AB - We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent. AU - Ajanki, Oskari H AU - Erdös, László AU - Krüger, Torben H ID - 429 IS - 1-2 JF - Probability Theory and Related Fields SN - 01788051 TI - Stability of the matrix Dyson equation and random matrices with correlations VL - 173 ER - TY - JOUR AB - We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the th Lyapunov exponent is finite and the st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part. AU - Sadel, Christian AU - Xu, Disheng ID - 6086 IS - 4 JF - Ergodic Theory and Dynamical Systems TI - Singular analytic linear cocycles with negative infinite Lyapunov exponents VL - 39 ER - TY - JOUR AB - Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N−1/2+ε and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N). AU - Bao, Zhigang AU - Erdös, László AU - Schnelli, Kevin ID - 6511 IS - 3 JF - Annals of Probability SN - 00911798 TI - Local single ring theorem on optimal scale VL - 47 ER - TY - JOUR AB - The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where S is a countable discrete metric space and 0