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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.06895 |
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| _version_ | 1866917391622995968 |
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| author | Cui, Shaoxuan Wang, Lingfei Jardon-Kojakhmetov, Hildeberto Johansson, Karl Henrik Cao, Ming |
| author_facet | Cui, Shaoxuan Wang, Lingfei Jardon-Kojakhmetov, Hildeberto Johansson, Karl Henrik Cao, Ming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06895 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Markov Chains and Random Walks with Memory on Hypergraphs: A Tensor-Based Approach Cui, Shaoxuan Wang, Lingfei Jardon-Kojakhmetov, Hildeberto Johansson, Karl Henrik Cao, Ming Systems and Control 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. |
| title | Markov Chains and Random Walks with Memory on Hypergraphs: A Tensor-Based Approach |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.06895 |