56 citations · 238 across the 48 of their papers we have counts for
23 papers · 1 filter
Uniform-in-Time and Uniform-in-Temperature Particle Approximations of Coulomb MMD Flows
Junho Lee, Promit Ghosal
We study particle approximations of maximum mean discrepancy (MMD) flows with the Coulomb kernel on the torus , , driven by thermal noise of strength .…
Entropic Selection Principle for Monge's Optimal Transport
Shrey Aryan, Promit Ghosal
We investigate the small regularization limit of entropic optimal transport when the cost function is the Euclidean distance in dimensions , and the marginal measures are ab…
Universality of Persistence of Random Polynomials
Promit Ghosal, Sumit Mukherjee
We investigate the probability that a random polynomial with independent, mean-zero and finite variance coefficients has no real zeros. Specifically, we consider a random polynomia…
High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance
Krishnakumar Balasubramanian, Promit Ghosal, Ye He
We derive high-dimensional scaling limits and fluctuations for the online least-squares Stochastic Gradient Descent (SGD) algorithm by taking the properties of the data generating…
Fractal geometry of the PAM in 2D and 3D with white noise potential
Promit Ghosal, Jaeyun Yi
We study the parabolic Anderson model (PAM) \begin{equation} {\partial \over \partial t}u(t,x) =\frac{1}{2}Δu(t,x) + u(t,x)ξ(x), \quad t>0, x\in \mathbb{R}^d, \quad \text{and} \qua…
Long and short time laws of iterated logarithms for the KPZ fixed point
Sayan Das, Promit Ghosal, Yier Lin
We consider the KPZ fixed point starting from a general class of initial data. In this article, we study the growth of the large peaks of the KPZ fixed point at a spatial point …
Moment Intermittency in the PAM with Asymptotically Singular Noise
Pierre Yves Gaudreau Lamarre, Promit Ghosal, Yuchen Liao
Let be a singular Gaussian noise on that is either white, fractional, or with the Riesz covariance kernel; in particular, there exists a scaling parameter s…
The ASEP speed process
Amol Aggarwal, Ivan Corwin, Promit Ghosal
For ASEP with step initial data and a second class particle started at the origin we prove that as time goes to infinity the second class particle almost surely achieves a velocity…
Rigidity of the Stochastic Airy Operator
Pierre Yves Gaudreau Lamarre, Promit Ghosal, Wenxuan Li +1
We prove that the spectrum of the stochastic Airy operator is rigid in the sense of Ghosh and Peres (Duke Math. J., 166(10):1789--1858, 2017) for Dirichlet and Robin boundary condi…
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}…
Law of Iterated Logarithms and Fractal Properties of the KPZ Equation
Sayan Das, Promit Ghosal
We consider the Cole-Hopf solution of the (1+1)-dimensional KPZ equation started from the narrow wedge initial condition. In this article, we ask how the peaks and valleys of the K…
Lyapunov exponents of the SHE for general initial data
Promit Ghosal, Yier Lin
We consider the -dimensional stochastic heat equation (SHE) with multiplicative white noise and the Cole-Hopf solution of the Kardar-Parisi-Zhang (KPZ) equation. We show an…
Probabilistic conformal blocks for Liouville CFT on the torus
Promit Ghosal, Guillaume Remy, Xin Sun +1
Virasoro conformal blocks are a family of important functions defined as power series via the Virasoro algebra. They are a fundamental input to the conformal bootstrap program for…
KPZ equation correlations in time
Ivan Corwin, Promit Ghosal, Alan Hammond
We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic PDE under the characteristic scaling of time, space and fluctuations. We study the correlation o…
Stochastic PDE limit of the dynamic ASEP
Ivan Corwin, Promit Ghosal, Konstantin Matetski
We study a stochastic PDE limit of the height function of the dynamic asymmetric simple exclusion process (dynamic ASEP). A degeneration of the stochastic Interaction Round-a-Face…
Limiting speed of a second class particle in ASEP
Promit Ghosal, Axel Saenz, Ethan C. Zell
We study the asymptotic speed of a second class particle in the two-species asymmetric simple exclusion process (ASEP) on with each particle belonging either to the fi…
KPZ equation tails for general initial data
Ivan Corwin, Promit Ghosal
We consider the upper and lower tail probabilities for the centered (by time) and scaled (according to KPZ time scaling) one-point distribution of the Cole-Hopf soluti…
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…
Stochastic PDE Limit of the Six Vertex Model
Ivan Corwin, Promit Ghosal, Hao Shen +1
We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter so as to zoom into the ferroelectric/disordered phase crit…
Lower tail of the KPZ equation
Ivan Corwin, Promit Ghosal
We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data. Our bounds hold for all sufficient…
Limit law of a second class particle in TASEP with non-random initial condition
Patrik L. Ferrari, Peter Nejjar, Promit Ghosal
We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density on and on , and a second c…
Correlation Functions of the Pfaffian Schur Process Using Macdonald Difference Operators
Promit Ghosal
We study the correlation functions of the Pfaffian Schur process. Borodin and Rains [J. Stat. Phys. 121 (2005), 291-317] introduced the Pfaffian Schur process and derived its corre…
Hall-Littlewood-PushTASEP and its KPZ limit
Promit Ghosal
We study a new model of interactive particle systems which we call the randomly activated cascading exclusion process (RACEP). Particles wake up according to exponential clocks and…