The speed of random walks on semigroups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909578741940224 |
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| author | Blachar, Guy Greenfeld, Be'eri |
| author_facet | Blachar, Guy Greenfeld, Be'eri |
| contents | We construct, for each real number $0\leq α\leq 1$, a random walk on a finitely generated semigroup whose speed exponent is $α$. We further show that the speed function of a random walk on a finitely generated semigroup can be arbitrarily slow, yet tending to infinity. These phenomena demonstrate a sharp contrast from the group-theoretic setting. On the other hand, we show that the distance of a random walk on a finitely generated semigroup from its starting position is infinitely often larger than a non-constant universal lower bound, excluding a certain degenerate case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The speed of random walks on semigroups Blachar, Guy Greenfeld, Be'eri Group Theory Combinatorics Probability We construct, for each real number $0\leq α\leq 1$, a random walk on a finitely generated semigroup whose speed exponent is $α$. We further show that the speed function of a random walk on a finitely generated semigroup can be arbitrarily slow, yet tending to infinity. These phenomena demonstrate a sharp contrast from the group-theoretic setting. On the other hand, we show that the distance of a random walk on a finitely generated semigroup from its starting position is infinitely often larger than a non-constant universal lower bound, excluding a certain degenerate case. |
| title | The speed of random walks on semigroups |
| topic | Group Theory Combinatorics Probability |
| url | https://arxiv.org/abs/2504.09633 |