3 citations · 3 across the 9 of their papers we have counts for
9 papers · 1 filter
Renormalizing small ball events for branching random walk
Vilas Winstein
Consider a branching random walk (BRW) of depth with standard Gaussian increments, conditioned on all endpoints lying in an interval of radius (which may depend on ), i.…
Correlation decay in area-tilted line ensembles
Shirshendu Ganguly, Vilas Winstein
Random surfaces on a hard substrate often exhibit entropic repulsion, wherein the surface is propelled upwards to allow entropically preferable downward fluctuations. A particularl…
The maximum-entropy median-martingale
Rikhav Shah, Vilas Winstein
This short note explores the maximum-entropy walk on the unit interval that is a median-martingale. That is, the median of its next state is equal to its current state. The station…
Wasserstein distances between ERGMs and Erdős-Rényi models
Vilas Winstein
Ferromagnetic exponential random graph models (ERGMs) are random graph models under which the presence of certain small structures (such as triangles) is encouraged; they can be co…
Approximate FKG inequalities for phase-bound spin systems, with applications to central limit theorems for exponential random graphs
Satyaki Mukherjee, Vilas Winstein
The Fortuin-Kasteleyn-Ginibre (FKG) inequality is an invaluable tool in monotone spin systems satisfying the FKG lattice condition, which provides positive correlations for all coo…
Decoupling of clusters in independent sets in a percolated hypercube
Mriganka Basu Roy Chowdhury, Shirshendu Ganguly, Vilas Winstein
Independent sets in graphs are sets of vertices containing no neighbors, and they represent a canonical spin system with hardcore constraints. Of particular interest is the setting…
Quantitative central limit theorems for exponential random graphs
Vilas Winstein
Ferromagnetic exponential random graph models (ERGMs) are nonlinear exponential tilts of Erdős-Rényi models, under which the presence of certain subgraphs such as triangles may be…
Concentration via metastable mixing, with applications to the supercritical exponential random graph model
Vilas Winstein
Folklore belief holds that metastable wells in low-temperature statistical mechanics models exhibit high-temperature behavior. We make this rigorous in the exponential random graph…
Gaussian to log-normal transition for independent sets in a percolated hypercube
Mriganka Basu Roy Chowdhury, Shirshendu Ganguly, Vilas Winstein
Independent sets in graphs, i.e., subsets of vertices where no two are adjacent, have long been studied, for instance as a model of hard-core gas. The -dimensional hypercube, $\…