Probability
Spring Organizer: Amir Dembo
Past Events
Gibbsian line ensembles have been the topic of much recent interest at the interface of probability and statistical physics, most prominently via the Airy line ensemble occurring as a scaling limit of Dyson Brownian motion. Recently, Caputo, Ioffe and Wachtel [CIW] have proposed an area-tilted…
Markov chains give natural approaches to sample from various distributions on independent sets of graphs. Considering the uniform distribution on independent sets of a fixed size k in a graph G, the corresponding Markov chain is the "down-up" walk. The down-up walk starts at an arbitrary…
It has been observed that wide neural networks (NNs) with randomly initialized weights may be well-approximated by Gaussian fields indexed by the input space of the NN, and taking values in the output space. There has been a flurry of recent work making this observation precise, since it sheds…
In KPZ universality, an important family of models arises from 2D last-passage percolation (LPP): in a 2D i.i.d. random field, one considers the geodesic connecting two vertices, which is defined as the up-right path maximizing its weight, i.e., the sum/integral of the random field along it. A…
The (2+1)D SOS model above a hard wall is a random surface studied in statistical mechanics, among other reasons, to approximate the interface in the 3D Ising model. I will discuss the problem of understanding scaling limits of the level lines of this surface, through the lens of Gibbsian line…
Determining the spectrum and eigenvectors of the adjacency matrix of random graphs is a fundamental problem with applications in computer science and statistical physics. Often, the relevant model is the Erdős-Rényi model, where edges are included independently with some fixed probability. In…
Prophet inequalities compare the expected performance of a stopping rule to a "prophet" who has complete knowledge of the future. The classical prophet inequality states that for a sequence of nonnegative random variables $X_1,\dots,X_n$ with known distributions, there is a stopping rule which…
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex with a latent feature vector sampled from a mixture of Gaussians, and we add edge if and only if the feature vectors are sufficiently…
The Coulomb gas is a statistical mechanical model of interacting electric point charges with connections to several areas of math and physics. I will motivate the model and give a simple relationship between the gas and systems of charged points and disks. Consequences of the relationship…
Given a task, is it better to be systematic or random? I will address this ill-posed question by studying the Gibbs sampler (Glauber dynamics). Should one systematically go through the coordinates in some order or just update at random? Surprisingly, in classes of examples where things can be…