Publications (54)
Fractal Geometry of the Valleys of the Parabolic Anderson Equation
Promit Ghosal, Jaeyun Yi
We study the macroscopic fractal properties of the deep valleys of the solution of the -dimensional parabolic Anderson equation $${\partial \over \partial t}u(t,x) =\frac{1}…
Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus
Harini Desiraju, Promit Ghosal, Andrei Prokhorov
The paper rigorously proves a conjectured exponential form for the semi‑classical limit of Liouville conformal blocks on a one‑punctured torus, establishing convergence and linking…
Spectral rigidity of random Schrödinger operators via Feynman-Kac formulas
Pierre Yves Gaudreau Lamarre, Promit Ghosal, Yuchen Liao
We develop a technique for proving number rigidity (in the sense of Ghosh-Peres) of the spectrum of general random Schrödinger operators (RSOs). Our method makes use of Feynman-Ka…
Clustering by Denoising: Latent plug-and-play diffusion for single-cell data
Dominik Meier, Shixing Yu, Sagnik Nandy +2
Single-cell RNA sequencing (scRNA-seq) enables the study of cellular heterogeneity. Yet, clustering accuracy, and with it downstream analyses based on cell labels, remain challengi…
Moments of the SHE under delta initial measure
Promit Ghosal
We give a rigorous proof of the contour integral formulas of the moments of the stochastic heat equation (SHE) started from the delta initial measure at the origin. These formulas…
The stochastic six vertex model and discrete orthogonal polynomial ensembles
Promit Ghosal, Guilherme L. F. Silva
Stochastic growth models in the Kardar-Parisi-Zhang (KPZ) universality class exhibit remarkable fluctuation phenomena. While a variety of powerful methods have led to a detailed un…