Probability Seminar Speaker: Vishesh Jain (University of Illinois Chicago) Title: Thresholds for edge colorings Abstract: We show that if each edge of the complete bipartite graph K_{n,n} is given a random list of C(\log n) colors from , then with high probability, there is a proper edge coloring where the color of each edge comes […]
Probability Seminar Speaker: Jean-Christophe Mourrat (ENS Lyon) Title: On the free energy of spin glasses with multiple types Abstract: In the simplest spin-glass model, due to Sherrington and Kirkpatrick, the energy function involves interaction terms between all pairs of spins. A bipartite version of this model can be obtained by splitting the spins into two […]
Probability Seminar Speaker: Wei-Kuo Chen (Minnesota) Title: Some rigorous results on the Lévy spin glass model Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin […]
Probability Seminar Speaker: Ahmed El Alaoui (Cornell) Title: Sampling from the SK and mixed p-spin measures with stochastic localization Abstract: I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for […]
Probability Seminar *Please note room change: Science Center 232* Speaker: Ron Peled (Tel Aviv University) Title: Localization for random band matrices Abstract: I will explain an approach via "an adaptive Mermin-Wagner style shift" which proves localization of N x N Gaussian random band matrices with band width W satisfying W << N^{1/4}. Joint work with Giorgio Cipolloni, Jeffrey […]
Probability Seminar Speaker: Emma Bailey (CUNY) Title: Large deviations of Selberg’s central limit theorem Abstract: Selberg’s CLT concerns the typical behaviour of the Riemann zeta function and shows that the random variable $\Re \log \zeta(1/2 + i t)$, for a uniformly drawn $t$, behaves as a Gaussian random variable with a particular variance. It is […]
Probability Seminar Speaker: Evita Nestoridi (Stonybrook) Title: Diagonalizing Transition Matrices of Card Shuffles Abstract: In their seminal work, Diaconis and Shahshahani used representation theory of the symmetric group to diagonalize the transition matrix of random transpositions. More recently, Dieker and Saliola introduced another technique to diagonalize the random-to-random card shuffle. In this talk we will […]
Probability Seminar Speaker: Jimmy He (MIT) Title: Boundary current fluctuations for the half space ASEP Abstract: The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space […]
Probability Seminar Speaker: Boris Hanin (Princeton) Title: Random Neural Networks Abstract: Fully connected neural networks are described two by structural parameters: a depth L and a width N. In this talk, I will present results and open questions about the asymptotic analysis of such networks with random weights and biases in the regime where N (and potentially […]
Probability Seminar Speaker: Giorgio Cipolloni (Princeton) Title: How do the eigenvalues of a large non-Hermitian random matrix behave? Abstract: We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a non-natural scale, due to strong correlations between the eigenvalues. Then, motivated by the […]
Probability Seminar Speaker: Marius Lemm, University of Tuebingen Title: Light cones for open quantum systems Abstract: We consider non-relativistic Markovian open quantum dynamics in continuous space. We show that, up to small probability tails, the supports of quantum states propagate with finite speed in any finite-energy subspace. More precisely, if the initial quantum state is localized […]
Probability Seminar Speaker: Arka Adhikari (Stanford) Title: Correlation decay for finite lattice gauge theories Abstract: In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. […]