Probability
Organizers: Amir Dembo & Brice Huang
Upcoming Events
I will discuss large deviations for the largest eigenvalue of random matrices, and specifically the spherical integral approach.
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How many distinct symbols should a password use if information about which symbols are used is leaked? For a password of fixed length n, the classical answer is roughly 0.72n. I will discuss some variants and their connections with condensation phenomena and equivalence of…
Random geometric graphs hide geometric structure inside an otherwise random-looking network: each vertex has a latent position on a high-dimensional sphere, and edges are formed between vertices that are sufficiently close. When can this hidden geometry be detected from the graph alone? In this…
In this talk, we consider the upper-tail large deviations of intersections of Brownian motions. Apart from intrinsic interest, these quantities are also closely related to the parabolic Anderson model via the Feynman-Kac formula. We prove that the occupation measures of Brownian motions…
Past Events
We discuss a recent result which makes early progress towards understanding temperature chaos in the Kardar–Parisi–Zhang universality class. We show that the appropriately centered and scaled free energy of positive temperature Continuum Directed Random Polymers (CDRPs) at distinct temperatures…
We study the statics and dynamics of the low-temperature ferromagnetic Ising model on random d-regular graphs. Dembo and Montanari (2010) showed that the model converges locally weakly to a 50/50-mixture of the plus and minus Gibbs measures on the infinite d-regular tree, and…
We study the large deviation principle (LDP) for a tensor-weighted functional of i.i.d. random variables, when the sequence of tensors converges under a variant of the "bad" cut norm. Using the LDP, we analyze a Gibbs measure with a tensor-valued Hamiltonian and characterize the optimizers of…
Permutons, which are probability measures on [0, 1]^2 with uniform marginals, are the natural scaling limits for sequences of (random) permutations. In particular, various classes of permutations arising from combinatorics and pattern avoidance have been shown to converge to universal permuton…
A mathematically precise definition of quantum field theories is a major and mostly unsolved goal of mathematical physics. One possible route to reaching this goal is through the program of constructive field theory, which is probabilistic at its core. This is one reason why there has been a…
A k-index model is a classical statistical model describing the dependency of a response variable y onto an input vector of covariates x. It posits that y depends on x only via its projection onto a k-dimensional subspace. Learning in this model boils down to estimating this subspace from data,…
In 2017, Miller computed the character tables of S_n for all n up to 38 and looked at various statistical properties of the entries. Characters of symmetric groups take only integer values, and based on his computations, Miller conjectured that almost all entries of the character table of S_n…
There is a close connection between certain models of random integer partitions and random growth models in the KPZ universality class. I will give an introduction to these connections before discussing some new work establishing non-trivial symmetries of two particular models of random…
Exponential random graph models (ERGMs) are exponential tilts of Erdos–Renyi models where higher-order interactions promote the presence of small subgraphs like triangles. These models exhibit metastable behavior at low temperatures (strong interaction) and decompose as mixtures of phase…
The dimer model refers to the study of random dimer covers (or perfect matchings) of a bipartite graph. A remarkable feature of these models is the emergence of limit shapes: in large periodic graphs, a random matching concentrates around a deterministic shape. Although general dimer models…