Year: 2024
Type: preprint
Abstract: Consider a discrete time Markov process $X^\varepsilon$ on $\mathbb R^d$ that makes a deterministic jump prescribed by a map $φ\colon \mathbb R^d \to \mathbb R^d$, and then takes a small Gaussian step of variance $\varepsilon^2$. For certain chaotic maps $φ$, the effective diffusivity of $X^\varepsilon$ may be bounded away from $0$ as $\varepsilon \to 0$. This is known as residual diffusivity, and in this paper we prove residual diffusivity occurs for a class of maps $φ$ obtained from piecewise affine expanding Bernoulli maps.
Source: arXiv (Cornell University)
Authors: Iyer, Gautam, Nolen, James
Institutions: Duke University, Carnegie Mellon University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4403747226