8 papers
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…
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…
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 ErdÅs-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…
Quantitative central limit theorems for exponential random graphs
Vilas Winstein
Ferromagnetic exponential random graph models (ERGMs) are nonlinear exponential tilts of ErdÅs-Rényi models, under which the presence of certain subgraphs such as triangles may b…
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…