Residual Diffusivity for Noisy Bernoulli Maps
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914952556576768 |
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| author | Iyer, Gautam Nolen, James |
| author_facet | Iyer, Gautam Nolen, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Residual Diffusivity for Noisy Bernoulli Maps Iyer, Gautam Nolen, James Dynamical Systems Analysis of PDEs Probability 60J05 (Primary) 37A25, 35B27 (Secondary) 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. |
| title | Residual Diffusivity for Noisy Bernoulli Maps |
| topic | Dynamical Systems Analysis of PDEs Probability 60J05 (Primary) 37A25, 35B27 (Secondary) |
| url | https://arxiv.org/abs/2409.12410 |