Rate of convergence of the critical point of the memory-τ self-avoiding walk in dimensions d>4
Abstract
We consider spread-out models of the self-avoiding walk and its finite-memory version, known as the memory-τ walk, which prohibits loops whose length is at most τ, in dimensions d>4. The critical point is defined as the radius of convergence of the generating function for each model. It is known that the critical point of the memory-τ walk is non-decreasing in τ and converges to that of the self-avoiding walk as τ tends to infinity. In this paper, we study the rate at which the critical point of the memory-τ walk converges to that of the self-avoiding walk and show that the order is τ−(d−2)∕2. The proof relies on the lace expansion, introduced by Brydges and Spencer.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
advanced mathematical theories
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–28
- Publication date
- 1 January 2026
- Language
- EN