Publication 24-CNA-012

Residual Diffusivity For Noisy Bernoulli Maps

Gautam Iyer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
gautam@math.cmu.edu

James Nolen
Department of Mathematics
Duke University
Durham, NC 27708
nolen@math.duke.edu

Abstract: Consider a discrete time Markov process $X^\epsilon$ on $\mathbb{R}^d$ that makes a deterministic jump prescribed by a map $\varphi$: $\mathbb{R}^d \rightarrow \mathbb{R}^d$, and then takes a small Gaussian step of variance $\epsilon^2$. For certain chaotic maps $\varphi$, the effective diffusivity of $X^\epsilon$ may be bounded away from 0 as $\epsilon \rightarrow 0$. This is known as residual diffusivity, and in this paper we prove residual diffusivity occurs for a class of maps $\varphi$ obtained from piecewise affine expanding Bernoulli maps.

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