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pro vyhledávání: '"Hermon, Jonathan"'
Motivated by the Asymptotic Equipartition Property and its recently discovered role in the cutoff phenomenon, we initiate the systematic study of varentropy on discrete groups. Our main result is an approximate tensorization inequality which asserts
Externí odkaz:
http://arxiv.org/abs/2409.16869
Autor:
Hermon, Jonathan, Huang, Xiangying
We consider the random Cayley graphs of a sequence of finite nilpotent groups of diverging sizes $G=G(n)$, whose ranks and nilpotency classes are uniformly bounded. For some $k=k(n)$ such that $1\ll\log k \ll \log |G|$, we pick a random set of genera
Externí odkaz:
http://arxiv.org/abs/2403.12355
For a finite graph $G=(V,E)$ let $G^*$ be obtained by considering a random perfect matching of $V$ and adding the corresponding edges to $G$ with weight $\varepsilon$, while assigning weight 1 to the original edges of $G$. We consider whether for a s
Externí odkaz:
http://arxiv.org/abs/2306.13077
Autor:
Hermon, Jonathan
We give a characterization of the relaxation time up to an absolute constant factor, in terms of stationary expected hitting times of large sets. This resolves a conjecture of Aldous and Fill. We give a similar characterization for the spectral profi
Externí odkaz:
http://arxiv.org/abs/2304.05878
We consider a variant of the configuration model with an embedded community structure and study the mixing properties of a simple random walk on it. Every vertex has an internal $\mathrm{deg}^{\text{int}}\geq 3$ and an outgoing $\mathrm{deg}^{\text{o
Externí odkaz:
http://arxiv.org/abs/2212.04469
We consider random walks on finite vertex-transitive graphs $\Gamma$ of bounded degree. We find a simple geometric condition which characterises the cover time fluctuations: the suitably normalised cover time converges to a standard Gumbel variable i
Externí odkaz:
http://arxiv.org/abs/2202.02255
Autor:
Hermon, Jonathan, Pymar, Richard
We consider the interchange process with $k$ particles (${\rm IP}(k)$) on $n$-vertex hypergraphs in which each hyperedge $e$ rings at rate $r_e$. When $e$ rings, the particles occupying it are permuted according to a random permutation from some arbi
Externí odkaz:
http://arxiv.org/abs/2105.13486
Publikováno v:
The Annals of Probability (2022), Vol. 50, No. 5, 1813-1884
In this paper we consider coalescing random walks on a general connected graph $G=(V,E)$. We set up a unified framework to study the leading order of the decay rate of $P_t$, the expectation of the fraction of occupied sites at time $t$, particularly
Externí odkaz:
http://arxiv.org/abs/2105.11585
Autor:
Hermon, Jonathan, Sousi, Perla
Let $P$ be an irreducible and reversible transition matrix on a finite state space $V$ with invariant distribution $\pi$. We let $k$ chains start by choosing independent locations distributed according to $\pi$ and then they evolve independently acco
Externí odkaz:
http://arxiv.org/abs/2104.00665
Autor:
Hermon, Jonathan, Olesker-Taylor, Sam
Consider the random Cayley graph of a finite group $G$ with respect to $k$ generators chosen uniformly at random, with $1 \ll \log k \ll \log |G|$; denote it $G_k$. A conjecture of Aldous and Diaconis (1985) asserts, for $k \gg \log |G|$, that the ra
Externí odkaz:
http://arxiv.org/abs/2102.02809