15:30 - 16:30, November 21, 2023 (Tuesday) R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Rate of Convergence of the Critical Point for the memory-$\tau$ Self-avoiding Walk in Dimension $d>4$. Noe Kawamoto (Hokkaido University)

Abstract

We consider the spread-out models of the self-avoiding walk and its finite-memory version, called the memory- walk. For both models, each step is uniformly distributed over the d-dimensional box . The critical point or the memory- walk is increasing in and converges to the critical point for the self-avoiding walk as goes to .

The speaker proved that the rate of convergence of in terms of is order of . Moreover, the speaker identified the exact expression of the coefficient of the dominant term of it. This improves the previous results obtained by Madras and Slade [Birkhäuser, The Self-Avoiding Walk, Lemma~6.8.6, 1993]. This talk is based on the speaker’s own work (https://arxiv.org/abs/2306.13936)