Open Access
2022 On the rate of escape or approach to the origin of a random string
Phúc Lâm
Author Affiliations +
Electron. Commun. Probab. 27: 1-13 (2022). DOI: 10.1214/22-ECP451


In this paper, we extend upon a result by Mueller and Tribe regarding Funaki’s model of a random string. Specifically, we examine the rate of escape of this model in dimensions d7. We also provide a bound for the rate of approach to the origin in dimension d=6.

Funding Statement

The author is supported by a Discover Grant for Undergraduate Summer Research at the University of Rochester.


The author would like to thank Carl Mueller for his mentorship and invaluable suggestions.


Download Citation

Phúc Lâm. "On the rate of escape or approach to the origin of a random string." Electron. Commun. Probab. 27 1 - 13, 2022.


Received: 25 September 2021; Accepted: 22 January 2022; Published: 2022
First available in Project Euclid: 28 January 2022

MathSciNet: MR4368695
Digital Object Identifier: 10.1214/22-ECP451

Primary: 60H15

Keywords: Rate of escape , recurrence , Stochastic heat equation

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