Related papers: The variational principle for a marked Gibbs point…
Large deviations principle is obtained for terminating multidimensional compound renewal processes. We also obtained the asymptotic of large deviations for the case when a Gibbs change of the original probability measure takes place. The…
In a recent work [Reible et al., Phys. Rev. Res. 5, 023156, 2023], it has been shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts, can be employed to estimate the size dependence…
We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
We develop a variational approach at finite temperature that incorporates many-body correlation self-consistently. The grand potential is constructed in terms of Green's function expressed by the variational parameters. We apply this…
This paper deals with stationary Gibbsian point processes on the plane with an interaction that depends on the tiles of the Delaunay triangulation of points via a bounded triangle potential. It is shown that the class of these Gibbs…
The finite-size critical properties of the ${\cal O}(n)$ vector $\phi^4$ model, with long-range interaction decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, are investigated. The system is confined to a…
We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given…
Gibbs random fields corresponding to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs with a certain summability property are constructed. It is proven that…
We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong combinatorial assumptions called ``finite irreducibility'' or ``finite primitiveness''. More precisely, we assume the…
We develop a new robust technique to deduce variance principles for non-integrable discrete systems. To illustrate this technique, we show the existence of a variational principle for graph homomorphisms from $\Z^m$ to a $d$-regular tree.…
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…
We prove a simple, explicit lower bound on the radius of a zero-free disk for Gibbs point processes defined by finite-range, repulsive multi-body interactions. Our lower bound improves on those previously known, and we demonstrate that it…
We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
We consider translation-invariant interacting particle systems on the lattice with finite local state space admitting at least one Gibbs measure as a time-stationary measure. The dynamics can be irreversible but should satisfy some mild…
A hierarchical model of interacting quantum particles performing anharmonic oscillations is studied in the Euclidean approach, in which the local Gibbs states are constructed as measures on infinite dimensional spaces. The local states…
We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…
We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…
Limit theorems, including the large deviation principle, are established for random point processes (fields), which describe the position distributions of the perfect boson gas in the regime of the Bose-Einstein condensation. We compare…