On Drift Induced by Local Transition Asymmetry in Combinatorial State Spaces

Fuente: arXiv
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Main Author: Ishizaki, Fumio
Format: Preprint
Published: 2026
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author Ishizaki, Fumio
author_facet Ishizaki, Fumio
contents We study stochastic processes on combinatorial state spaces with local transition constraints, as arise in local search algorithms. We show that asymmetry in local transitions induces a systematic drift in a distance process relative to a reference configuration. This drift results from the imbalance between inward and outward transitions, translating combinatorial multiplicities into directional bias. Analyzing the random walk on the Johnson graph, we derive explicit expressions for the drift and expected hitting times. We also show that locality constraints lead to trajectory-level differences that can hinder search trajectories from reaching the target, even under identical stationary distributions.
format Preprint
id arxiv_https___arxiv_org_abs_2604_17332
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On Drift Induced by Local Transition Asymmetry in Combinatorial State Spaces
Ishizaki, Fumio
Computational Engineering, Finance, and Science
Probability
We study stochastic processes on combinatorial state spaces with local transition constraints, as arise in local search algorithms. We show that asymmetry in local transitions induces a systematic drift in a distance process relative to a reference configuration. This drift results from the imbalance between inward and outward transitions, translating combinatorial multiplicities into directional bias. Analyzing the random walk on the Johnson graph, we derive explicit expressions for the drift and expected hitting times. We also show that locality constraints lead to trajectory-level differences that can hinder search trajectories from reaching the target, even under identical stationary distributions.
title On Drift Induced by Local Transition Asymmetry in Combinatorial State Spaces
topic Computational Engineering, Finance, and Science
Probability
url https://arxiv.org/abs/2604.17332