{"title":"On the Radius of Self-Repellent Fractional Brownian Motion","authors":"","doi":"10.1007/s10955-023-03227-y","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We study the radius of gyration <span> <span>\\(R_T\\)</span> </span> of a self-repellent fractional Brownian motion <span> <span>\\(\\left\\{ B^H_t\\right\\} _{0\\le t\\le T}\\)</span> </span> taking values in <span> <span>\\(\\mathbb {R}^d\\)</span> </span>. Our sharpest result is for <span> <span>\\(d=1\\)</span> </span>, where we find that with high probability, <span> <span>$$\\begin{aligned} R_T \\asymp T^\\nu , \\quad \\text {with }\\quad \\nu =\\frac{2}{3}\\left( 1+H\\right) . \\end{aligned}$$</span> </span>For <span> <span>\\(d>1\\)</span> </span>, we provide upper and lower bounds for the exponent <span> <span>\\(\\nu \\)</span> </span>, but these bounds do not match.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10955-023-03227-y","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
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 \(\mathbb {R}^d\). 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.
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.