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- W4366999422 abstract "Markov random fields on a countable set $sf V$ are studied. They are canonically set by a specification $gamma$, for which the dependence structure is defined by a pre-modification $(h_e)_{ein {sf E}}$ -- a consistent family of functions $h_e : S^eto [0,+infty)$, where $S$ is a standard Borel space and $sf E$ is an infinite collection of finite $esubset {sf V}$. Different $e$ may contain distinct number of elements, which, in particular, means that the dependence graph ${sf H}=({sf V}, {sf E})$ is a hypergraph. Given $ein {sf E}$, let $delta (e)$ be the logarithmic oscillation of $h_e$. The result of this work is the assertion that the set of all fields $mathcal{G}(gamma)$ is a singleton whenever $delta(e)$ satisfies a condition, a particular version of which can be $delta(e) leq varkappa g(n_{sf L}(e))$, holding for all $e$ and some $sf H$-specific $varkappain (0,1)$. Here $g$ is an increasing function, e.g., $g(n) = a+log n$, and $n_{sf L}(e)$ is the degree of $e$ in the line-graph ${sf L}({sf H})$, which may grow ad infinitum. This uniqueness condition is essentially less restrictive than those based on classical Dobrushin's methods, according to which either of $|e|$, $n_{sf L}(e)$ and $delta(e)$ should be globally bounded. We also prove that its fulfilment implies that the unique element of $mathcal{G}(gamma)$ is globally Markov." @default.
- W4366999422 created "2023-04-27" @default.
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- W4366999422 date "2023-04-22" @default.
- W4366999422 modified "2023-10-17" @default.
- W4366999422 title "Uniqueness of Markov random fields with higher-order dependencies" @default.
- W4366999422 doi "https://doi.org/10.48550/arxiv.2304.11369" @default.
- W4366999422 hasPublicationYear "2023" @default.
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