Residual Diffusivity for Noisy Bernoulli Maps

Gautam Iyer; James Nolen

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arXiv · 2409.12410

Residual Diffusivity for Noisy Bernoulli Maps

Gautam Iyer·James Nolen

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Abstract

Consider a discrete time Markov process $X^\varepsilon$ on $\mathbb R^d$ that makes a deterministic jump prescribed by a map $\varphi \colon \mathbb R^d \to \mathbb R^d$, and then takes a small Gaussian step of variance $\varepsilon^2$. For certain chaotic maps $\varphi$, 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 $\varphi$ obtained from piecewise affine expanding Bernoulli maps.

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BibTeX RIS

Gautam Iyer, James Nolen. 2024-09-19. Residual Diffusivity for Noisy Bernoulli Maps. https://arxiv.org/abs/2409.12410

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