N. Kawamoto

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20222026

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math.PR2026

Range convergence and sharp one-arm asymptotics for the critical percolation cluster in high dimensions

M. Cabezas, D. Croydon, A. Fribergh +1

For critical Bernoulli bond percolation on $Z^{d}$ in the high-dimensional regime, we prove that the rescaled empirical measure of the cluster of the origin converges, in a suitable…

math.PR2025

Asymptotic expansion of the critical point for oriented percolation in high dimensions

Noe Kawamoto

We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on $Z^{d}$ in powers of $d^{- 1}$ as $d \to \infty$ . The proof reli…

math.PR2023

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

Noe Kawamoto

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 dimension…

math.PR2022

Spread-out limit of the critical points for lattice trees and lattice animals in dimensions d>8

Noe Kawamoto, Akira Sakai

A spread-out lattice animal is a finite connected set of edges in ${{x, y} \subset Z^{d} : 0 < ∣∣ x - y ∣∣ \leq L}$ . A lattice tree is a lattice animal with no loops.The best est…

Range convergence and sharp one-arm asymptotics for the critical percolation cluster in high dimensions

Asymptotic expansion of the critical point for oriented percolation in high dimensions

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

Spread-out limit of the critical points for lattice trees and lattice animals in dimensions d>8

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