33. chen.kuzgun.ea:23:on

33. chen.kuzgun.ea:23:on#

On the radius of self-repellent fractional Brownian motion

Le Chen, Sefika Kuzgun, Carl Mueller, and Panqiu Xia

  • To appear in Journal of Statistical Physics

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,

\[R_T \asymp T^\nu, \quad \text{with } \nu=\frac{2}{3}(1+H).\]

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

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[] Le Chen, Sefika Kuzgun, Carl Mueller & Panqiu Xia (2023) ‘On the radius of self-repellent fractional Brownian motion’, preprint arXiv:2308.10889

MSC 2010 subject classifications: Primary 60H15. Secondary 35R60.

Keywords: fractional Brownian motion, self-avoiding, self-repellent, Girsanov theorem.

@article{chen.kuzgun.ea:23:on,
  title         = {On the radius of self-repellent fractional Brownian motion},
  author        = {Le Chen and Sefika Kuzgun and Carl Mueller and Panqiu Xia},
  year          = {2024},
  month         = {January},
  journal       = {Journal of Statistical Physics},
  url           = {https://link.springer.com/article/10.1007/s10955-023-03227-y}
}

References: Adler and Taylor [AT07]; Bauerschmidt et al. [BDCGS12]; Biagini et al. [BHZ08]; Biswas and Cherayil [BC95b]; Bock et al. [BBC+15]; Bolthausen [Bol90]; Bornales et al. [BOS13]; Brydges and Spencer [BS85]; Domb and Joyce [DJ72]; Edwards [Edw65]; Fixman [Fix62]; Greven and den Hollander [GdH93]; Grothaus et al. [GOdSS11]; Hara and Slade [HS91]; Hara and Slade [HS92]; Hu and Nualart [HN05]; Madras [Mad14]; Madras and Slade [MS93]; Mueller and Neuman [MN23]; Norros et al. [NVV99]; Rosen [Ros87]; Slade [Sla19];

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