Self-intersection local times of random fields in stochastic flows

TL;DR

This paper investigates how stochastic flows transform Gaussian fields on the plane, focusing on the existence and asymptotic behavior of self-intersection local times of the transformed fields.

Contribution

It establishes the existence of self-intersection local times for Gaussian fields under stochastic flow transformations and analyzes their asymptotic properties.

Findings

Existence of self-intersection local times for transformed Gaussian fields.

Asymptotic behavior of these local times is characterized.

Applicable to nonsmooth Gaussian fields with multiple self-intersections.

Abstract

In this article we study transformations of Gaussian field by stochastic flow on the plane. A stochastic flow is a solution to the equation with interaction whose coefficients depend on the occupation measure of the field. We consider nonsmooth Gaussian field, which has self-intersection local times of any multiplicity. In the article we prove the existence of self-intersection local times for the transformed field and study its asymptotics.