Essential sets for random operators constructed from Arratia flow

TL;DR

This paper investigates a strong random operator derived from Arratia flow, identifying a compact set in L2(R) that remains invariant under the operator and estimating its Kolmogorov widths, contributing to the understanding of random operators.

Contribution

It introduces a specific compact set in L2(R) that persists under the Arratia flow-based operator and provides estimates for its Kolmogorov widths, a novel analysis in this context.

Findings

Identified a compact set in L2(R) invariant under the operator.

Estimated the Kolmogorov widths of this set.

Provided insights into the structure of random operators from Arratia flow.

Abstract

In this paper we consider a strong random operator $T_t$ which describes shift of functions from $L_2(\mathbb{R})$ along an Arratia flow. We find a compact set in $L_2(\mathbb{R})$ that doesn't disappear under $T_t$, and estimate its Kolmogorov widths.