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arXiv · 2604.06895

Markov Chains and Random Walks with Memory on Hypergraphs: A Tensor-Based Approach

Shaoxuan Cui·Lingfei Wang·Hildeberto Jardon-Kojakhmetov·Karl Henrik Johansson·Ming Cao
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Abstract

Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains with memory. Our formulation introduces an even-order paired tensor that links folded and unfolded dynamics and characterizes their steady states and convergence. We further show that a Markov chain with memory can be approximated by a low-dimensional nonlinear tensor-based system and then provide a full system analysis. As an application, we define random walks on hypergraphs where memory naturally arises from the hyperedge structure, providing new tools for analyzing higher-order networks with time-dependent effects.

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Shaoxuan Cui, Lingfei Wang, Hildeberto Jardon-Kojakhmetov, Karl Henrik Johansson, Ming Cao. 2026-04-08. Markov Chains and Random Walks with Memory on Hypergraphs: A Tensor-Based Approach. https://arxiv.org/abs/2604.06895

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