Related papers: Sharp phase transition for random loop models on t…

In this paper we study random linear systems with $k$ variables per equation over the finite field GF(2), or equivalently $k$-XOR-CNF formulas. In a previous paper Creignou and Daud\'e proved that the phase transition for the consistency…

We investigate the statistics of extremal path(s) (both the shortest and the longest) from the root to the bottom of a Cayley tree. The lengths of the edges are assumed to be independent identically distributed random variables drawn from a…

Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…

We consider the interacting particle system on the homogeneous tree of degree $(d + 1)$, known as frog model. In this model, active particles perform independent random walks, awakening all sleeping particles they encounter, and dying after…

We consider a model of random loops on Galton-Watson trees with an offspring distribution with high expectation. We give the configurations a weighting of $\theta^{\#\text{loops}}$. For many $\theta>1$ these models are equivalent to certain…

In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated…

A little over 25 years ago Pemantle pioneered the study of the contact process on trees, and showed that the critical values $\lambda_1$ and $\lambda_2$ for global and local survival were different. Here, we will consider the case of trees…

We consider trap models on Z^d, namely continuous time Markov jump process on Z^d with embedded chain given by a generic discrete time random walk, and whose mean waiting time at x is given by tau_x, with tau = (tau_x, x in Z^d) a family of…

The $k$-section width and the Max-Cut for the configuration model are shown to exhibit phase transitions according to the values of certain parameters of the asymptotic degree distribution. These transitions mirror those observed on…

Consider a sequence (indexed by n) of Markov chains Z^n in R^d characterized by transition kernels that approximately (in n) depend only on the rescaled state n^{-1} Z^n. Subject to a smoothness condition, such a family can be closely…

We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. The D_q-spectrum of the invariant measure of this effective…

We consider the frog model with geometric lifetime (parameter $1-p$) on homogeneous trees of dimension $d$. In 2002, \cite{alves2002-2} proved that there exists a critical lifetime parameter $p_c\in(0,1)$ above which infinitely many frogs…

A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…

We derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-$\alpha$ (Ly-$\alpha$) forest flux fluctuations. The algorithm exploits the unique geometry of Ly-$\alpha$ forest data to efficiently measure…

Families of symmetric simple random walks on Cayley graphs of Abelian groups with a bound on the number of generators are shown to never have sharp cut off in the sense of [1], [3], or [5]. Here convergence to the stationary distribution is…

The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…

This paper studies the behavior of RWRE on trees in the critical case left open in previous work. For trees of exponential growth, a random perturbation of the transition probabilities can change a transient random walk into a recurrent…

We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…

We show that the spontaneous symmetry breaking can be defined also for finite systems based on the properly defined jump probability between the ground states in the 2d and 3d Ising models on a square and a cubic lattice respectively. Our…