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 . We also provide a bound for the rate of approach to the origin in dimension .
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.
"On the rate of escape or approach to the origin of a random string." Electron. Commun. Probab. 27 1 - 13, 2022. https://doi.org/10.1214/22-ECP451