arXiv subjects

Kenji Kimura

Publications and source records attributed to Kenji Kimura.

4 recordsLinked to original sources

arXiv2023

A necessary and sufficient condition for the existence of a properly coloured $f$-factor in an edge-coloured graph

The main result of this paper is an edge-coloured version of Tutte's $f$-factor theorem. We give a necessary and sufficient condition for an edge-coloured graph $G^c$ to have a properly coloured $f$-factor. We state and prove our result in terms of an auxiliary graph $G_f^c$ which has a 1-factor if and only if $G^c$ has a properly coloured $f$-factor; this is analogous to the "short proof" of the $f$-factor theorem given by Tutte in 1954. An alternative statement, analogous to the original $f$-factor theorem, is also given. We show that our theorem generalises the $f$-factor theorem; that is, the former implies the latter. We consider other properties of edge-coloured graphs, and show that similar results are unlikely for $f$-factors with rainbow components and distance-$d$-coloured $f$-factors, even when $d=2$ and the number of colours used is asymptotically minimal.

math.CO↗

arXiv2017

Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1,2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.

cond-mat.stat-mech↗

arXiv2016

Extension of the constant exchange probability method to multi-dimensional replica exchange Monte Carlo applied to the tri-critical spin-1 Blume-Capel model

In replica exchange Monte Carlo (REM), tuning of the temperature set and the exchange scheduling are crucial in improving the accuracy and reducing calculation time. In multi-dimensional simulated tempering, the first order phase transition is accessible. Therefore it is important to study the tuning of parameter set and the scheduling of exchanges in the parallel counterpart, the multi-dimensional REM. We extend Hukushima's constant exchange probability method to multi-dimensional REM for the parameter set. We further propose a combined method to use this set and the Bittner-Nussbaumer-Janke's PT tau algorithm for scheduling. We test the proposed method in two-dimensional spin-1 Blume-Capel model and find that it works efficiently, including the vicinity of the first order phase transition.

cond-mat.stat-mech↗

arXiv2016

Monte Carlo estimation of the number of tatami tilings

Motivated by the way Japanese tatami mats are placed on the floor, we consider domino tilings with a constraint and estimate the number of such tilings of plane regions. We map the system onto a monomer-dimer model with a novel local interaction on the dual lattice. We use a variant of the Hamiltonian replica exchange Monte Carlo method and the multi-parameter reweighting technique to study the model. The properties of the quantity are studied beyond exact enumeration and combinatorial method. The logarithm of the number of the tilings is linear in the boundary length of the region for all the regions studied.

cond-mat.stat-mech↗