Related papers: Gibbsianness of locally thinned random fields
We consider the i.i.d. Bernoulli field $\mu_p$ on $\mathbb{Z}^d$ with occupation density $p\in [0,1]$. To each realization of the set of occupied sites we apply a thinning map that removes all occupied sites that are isolated in graph…
We consider the i.i.d. Bernoulli field $\mu_p$ with occupation density $p \in (0,1)$ on a possibly non-regular countably infinite tree with bounded degrees. For large $p$, we show that the quasilocal Gibbs property, i.e. compatibility with…
This paper investigates the thinned Bernoulli field (TBF) on the one-dimensional integer lattice, where isolated occupied sites are removed from a standard Bernoulli configuration with density $p$. Our present work complements previous…
We consider fermion (or determinantal) random point fields on Euclidean space $\mbR^d$. Given a bounded, translation invariant, and positive definite integral operator $J$ on $L^2(\mbR^d)$, we introduce a determinantal interaction for a…
Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main…
Many Gibbs measures with mean field interactions are known to be chaotic, in the sense that any collection of $k$ particles in the $n$-particle system are asymptotically independent, as $n\to\infty$ with $k$ fixed or perhaps $k=o(n)$. This…
In the language of random counting measures many structural properties of the Poisson process can be studied in arbitrary measurable spaces. We provide a similarly general treatise of Gibbs processes. With the GNZ equations as a definition…
We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a…
We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local…
Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To…
In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential…
The Markov property entails the conditional independence structure inherent in Gibbs distributions for general classical Hamiltonians, a feature that plays a crucial role in inference, mixing time analysis, and algorithm design. However,…
We investigate the hyperuniformity of marked Gibbs point processes with weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Some variants of stability and range assumptions are posed on the…
We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…
We restore part of the thermodynamic formalism for some renormalized measures that are known to be non-Gibbsian. We first point out that a recent theory due to Pfister implies that for block-transformed measures free energies and relative…
In this paper, we detail and complete the existing characterizations of the decimation of the Ising model on $\Z^2$ in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and…
Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…
This paper investigates the feasibility of mapping non-local, sparse, diagonal forms of quantum Hamiltonians to local forms via eigenbasis permutations. We prove that such a mapping is not always possible, definitively refuting the…
We consider the problem of embedding one i.i.d.\ collection of Bernoulli random variables indexed by $\mathbb{Z}^d$ into an independent copy in an injective $M$-Lipschitz manner. For the case $d=1$, it was shown by Basu and Sly (PTRF, 2014)…
We consider the continuum Widom-Rowlinson model under independent spin-flip dynamics and investigate whether and when the time-evolved point process has an (almost) quasilocal specification (Gibbs-property of the time-evolved measure). Our…