Related papers: Phase transition in random contingency tables with…
Localization of electrons in 1D disordered systems is usually described in the random phase approximation, when distributions of phases \varphi and \theta, entering the transfer matrix, are considered as uniform. In the general case, the…
We show that a randomly perturbed digraph, where we start with a dense digraph $D_\alpha$ and add a small number of random edges to it, will typically contain a fixed orientation of a bounded degree spanning tree. This answers a question…
Abrupt transition to turbulence may occur in pipe and channel flows at moderate flow rates, an unexpected event according to linear stability theory, and has been an open problem in fluid dynamics for more than a century. Extensive…
We consider first passage percolation on certain isotropic random graphs in $\mathbb{R}^d$. We assume exponential concentration of passage times $T(x,y)$, on some scale $\sigma_r$ whenever $|y-x|$ is of order $r$, with $\sigma_r$ "growning…
The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\alpha$. For this point process, we obtain 1) exponential moment…
We consider the number distribution of topological defects resulting from the finite-time crossing of a continuous phase transition and identify signatures of universality beyond the mean value, predicted by the Kibble-Zurek mechanism.…
We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site $i=1,...,N$ is occupied by a particle of type $\a=A,B,C,$ with the average density of each particle species…
We analyze the component evolution in inhomogeneous random intersection graphs when the average degree is close to 1. As the average degree increases, the size of the largest component in the random intersection graph goes through a phase…
Consider the complete graph on \(n\) vertices where each edge is independently open with probability \(p,\) or closed otherwise. Phase transitions for such graphs for \(p = \frac{C}{n}\) have previously been studied using techniques like…
We consider an analogue of the Kac random walk on the special orthogonal group $SO(N)$, in which at each step a random rotation is performed in a randomly chosen 2-plane of $\bR^N$. We obtain sharp asymptotics for the rate of convergence in…
We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…
We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behaviours of the shattering times, defined as the first instants when all the blocks of…
A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…
In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph.…
Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within…
We study a non-Anderson disorder driven quantum phase transition in a semi-infinite Dirac semimetal with a flat boundary. The conformally invariant boundary conditions, which include those that are time-reversal invariant, lead to…
We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. This is an old question which relates to recent advances in copula modeling for discrete random…
We prove the sharpness of the phase transition for speed in the biased random walk on the supercritical percolation cluster on Z^d. That is, for each d at least 2, and for any supercritical parameter p > p_c, we prove the existence of a…
Motivated by the Beck-Fiala conjecture, we study the discrepancy problem in two related models of random hypergraphs on $n$ vertices and $m$ edges. In the first (edge-independent) model, a random hypergraph $H_1$ is constructed by fixing a…
We consider the single-file dynamics of $N$ identical random walkers moving with diffusivity $D$ in one dimension (walkers bounce off each other when attempting to overtake). Additionally, we require that the separation between neighboring…