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Rate of convergence of the critical point of the memory-τ self-avoiding walk in dimensions d>4

Noe Kawamoto

Electronic Journal of Probability2026https://doi.org/10.1214/26-ejp1486article
ABDC A
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0.50

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.

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https://doi.org/https://doi.org/10.1214/26-ejp1486

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@article{noe2026,
  title        = {{Rate of convergence of the critical point of the memory-τ self-avoiding walk in dimensions d>4}},
  author       = {Noe Kawamoto},
  journal      = {Electronic Journal of Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/26-ejp1486},
}

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