arXiv subjects

Noe Kawamoto

Publications and source records attributed to Noe Kawamoto.

4 recordsLinked to original sources

arXiv2026

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

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.

math.PR↗

arXiv2025

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

We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on $\mathbb Z^d$ in powers of $d^{-1}$ as $d\rightarrow \infty$. The proof relies heavily on the lace expansion.

math.PR↗

arXiv2023

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

A spread-out lattice animal is a finite connected set of edges in $\{ \{x,y\} \subset \mathbb{Z}^d:0<||x-y||\le L \}$. A lattice tree is a lattice animal with no loops.The best estimate on the critical point $p_c$ so far was achieved by Penrose(JSP,77(1994):3-15): $p_c=1/e+O(L^{-2d/7}\log L)$ for both models for all $d\ge1$. In this paper, we show that $p_c=1/e+CL^{-d}+O(L^{-d-1})$ for all $d>8$, where the model-dependent constant $C$ has the random-walk representation $C_\mathrm{LT}=\sum_{n=2}^\infty\frac{n+1}{2e}U^{*n}(o)$ and $C_\mathrm{LA}=C_\mathrm{LT}-\frac1{2e^2}\sum_{n=3}^\infty U^{*n}(o)$, where $U^{*n}$ is the $n$-fold convolution of the uniform distribution on the $d$-dimensional ball $\{x\in \mathbb{R}^d:\|x\|\le1\}$. The proof is based on a novel use of the lace expansion for the two-point function and detailed analysis of the 1-point function at a certain value of $p$ that is designed to make the analysis extreamly simple.

math.PR↗

arXiv2023

Mathematical aspects of the Digital Annealer's simulated annealing algorithm

The Digital Annealer is a CMOS hardware designed by Fujitsu Laboratories for high-speed solving of Quadratic Unconstrained Binary Optimization (QUBO) problems that could be difficult to solve by means of existing general-purpose computers. In this paper, we present a mathematical description of the first-generation Digital Annealer's Algorithm from the Markov chain theory perspective, establish a relationship between its stationary distribution with the Gibbs-Boltzmann distribution, and provide a necessary and sufficient condition on its cooling schedule that ensures asymptotic convergence to the ground states.

math.OC↗