论自斥力分形布朗运动的半径

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Statistical Physics Pub Date : 2024-01-31 DOI:10.1007/s10955-023-03227-y

Le Chen, Sefika Kuzgun, Carl Mueller, Panqiu Xia

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引用次数: 0

摘要

Abstract We study the radius of gyration $R_T$ of a self-repellent fractional Brownian motion $\left\{ B^H_t\right\} _{0\le t\le T}$ taking values in $\mathbb {R}^d$ .我们最尖锐的结果是针对（d=1）的，在这里我们发现很有可能， $$\begin{aligned}R_T \asymp T^\nu , \quad \text {with }\quad \nu =\frac{2}{3}\left( 1+H\right).\end{aligned}$$ 对于 $d>1$, 我们提供了指数 $\nu $ 的上下限，但是这些界限并不匹配。

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On the Radius of Self-Repellent Fractional Brownian Motion

We study the radius of gyration $R_T$ of a self-repellent fractional Brownian motion $\left\{ B^H_t\right\} _{0\le t\le T}$ taking values in $\mathbb {R}^d$. Our sharpest result is for $d=1$, where we find that with high probability,

$$\begin{aligned} R_T \asymp T^\nu , \quad \text {with }\quad \nu =\frac{2}{3}\left( 1+H\right) . \end{aligned}$$

For $d>1$, we provide upper and lower bounds for the exponent $\nu $, but these bounds do not match.

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来源期刊

Journal of Statistical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

12.50%

发文量

152

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.