Random Lipschitz functions on graphs with weak expansion
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915020492767232 |
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| author | Işık, Senem Park, Jinyoung |
| author_facet | Işık, Senem Park, Jinyoung |
| contents | Benjamini, Yadin, and Yehudayoff (2007) showed that if the maximum degree of a graph $G$ is 'sub-logarithmic,' then the typical range of random $\mathbb Z$-homomorphisms is super-constant. Furthermore, they showed that there is a sharp transition on the range of random $\mathbb Z$-homomorphisms on the graph $C_{n,k}$, the tensor product of the $n$-cycle and the complete graph on $k$ vertices with self-loops, around $k=2\log n$. We extend (to some extent) their results to random $M$-Lipschitz functions and random real-valued Lipschitz functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_09640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random Lipschitz functions on graphs with weak expansion Işık, Senem Park, Jinyoung Probability Mathematical Physics Combinatorics 60C05 Benjamini, Yadin, and Yehudayoff (2007) showed that if the maximum degree of a graph $G$ is 'sub-logarithmic,' then the typical range of random $\mathbb Z$-homomorphisms is super-constant. Furthermore, they showed that there is a sharp transition on the range of random $\mathbb Z$-homomorphisms on the graph $C_{n,k}$, the tensor product of the $n$-cycle and the complete graph on $k$ vertices with self-loops, around $k=2\log n$. We extend (to some extent) their results to random $M$-Lipschitz functions and random real-valued Lipschitz functions. |
| title | Random Lipschitz functions on graphs with weak expansion |
| topic | Probability Mathematical Physics Combinatorics 60C05 |
| url | https://arxiv.org/abs/2411.09640 |