Related papers: On $P$-adic Ising-Vannimenus model on an arbitrary…

We study the nonequilibrium properties of directed Ising models with non conserved dynamics, in which each spin is influenced by only a subset of its nearest neighbours. We treat the following models: (i) the one-dimensional chain; (ii) the…

A new approach to the solution of quasilinear nonelliptic first-order systems of inhomogeneous PDEs in many dimensions is presented. It is based on a version of the conditional symmetry and Riemann invariant methods. We discuss in detail…

In this paper we shall consider the connections between Lyapunov integral operators and Gibbs measures for four competing interactions of models with uncountable (i.e. $[0,1]$) set of spin values on a Cayley tree. And we shall prove the…

We give an equivalent condition for the existence of invariant Gibbs measures for sequences of continuous functions on one-sided subshifts and, more generally, for the existence of Gibbs measures. These extend the results of Kim [6] and…

The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here the latter model is studied on a…

In this paper, we consider an Ising model with three competing interactions on a triangular chandelier-lattice (TCL). We describe the existence, uniqueness, and non-uniqueness of translation-invariant Gibbs measures associated with the…

In this paper we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact and negatively curved basis. We also develop a notion of $F$-harmonic measure and prove that there exists a natural…

We consider both Hard-Core and Soft-Core Widom-Rowlinson models with spin values $-1,0,1$ on a Cayley tree of order $k\geq 2$ and we are interested in the Gibbs measures of the models. The models depend on 3 parameters: the order $k$ of the…

We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic…

In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., p_c < p_u. Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical…

We consider Gibbs measures relative to Brownian motion of Feynman-Kac type, with single site potential V. We show that for a large class of V, including the Coulomb potential, there exist infinitely many infinite volume Gibbs measures.

In 1993 van den Berg and Kesten proved a strict monotonicity theorem for first passage percolation on $\mathbb{Z}^d$, $d \ge 2$: given two probability measures $\nu$ and $\tilde{\nu}$ with finite mean, if $\tilde{\nu}$ is strictly more…

We present a novel way of realizing the Bernoulli shift on $p$ symbols on the $p$-adic integers, where $p$ is a prime. By showing that suitably small perturbations of the shift are still Bernoulli we find many "nice" maps, such as…

Considerations of the bad-metal behavior led to an early proposal for a quantum critical point under a P for As doping in the iron pnictides, which has since been experimentally observed. We study here an effective model for the…

Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…

We explicitly determine all of the transitive groups of degree p-squared, p a prime, whose Sylow p-subgroup is not the wreath product of two cyclic groups of order p. Furthermore, we provide a general description of the transitive groups of…

In this paper we study percolation on a roughly transitive graph G with polynomial growth and isoperimetric dimension larger than one. For these graphs we are able to prove that p_c < 1, or in other words, that there exists a percolation…

We classify the invariant Borel measures for adic transformations, where the alphabets have bounded size and the measure is finite on the path space of some sub-Bratteli diagram. We develop a nonstationary version of the Frobenius normal…

We present here a PAC-Bayesian point of view on adaptive supervised classification. Using convex analysis, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior…

Motivated by applications in medical bioinformatics, Khayatian et al. (2024) introduced a family of metrics on Cayley trees (the $k$-RF distance, for $k=0, \ldots, n-2$) and explored their distribution on pairs of random Cayley trees via…