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math.PR2024
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…
math.PR2023
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…
math.PR2022★ 3 cited
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 …