Probability
Organizers: Amir Dembo
Upcoming Events
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,…
Past Events
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…
We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in the scaling behavior of these fluctuations, leading to…
Polymers in disordered media are examples of random Gibbs measures on directed paths moving through a random environment. Such disordered systems often exhibit complex landscape behavior rich with multiple valleys which act as metastable states. This generic property manifests in multiple forms…
In this talk, I will discuss the construction of the Yang-Mills-Higgs measure on the two-dimensional torus. In the 1980s, Parisi and Wu proposed a dynamical approach to constructing such measure via the corresponding Langevin dynamics, aiming to sidestep the difficulty of fixing a global gauge.…
In this talk we discuss some results describing the fluctuation scaling limits for some interacting particle systems.
Dimer models (random lozenge or domino tilings) on large planar domains exhibit universality behavior: local convergence to translation-invariant Gibbs measures, global fluctuations described by the Gaussian Free Field (GFF), and Airy line ensemble at the edges. In this talk, I discuss two…
In this talk, we consider the asymmetric simple exclusion process with open boundaries (open ASEP). We give an overview on recent results on mixing times for the open ASEP. In particular, we discuss mixing times for the open ASEP at the triple point.
This talk is based on joint work with…