Related papers: Two-dimensional random interlacements: 0-1 law and…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…
Given $\omega\ge 1$, let $Z^2_{(\omega)}$ be the graph with vertex set $Z^2$ in which two vertices are joined if they agree in one coordinate and differ by at most $\omega$ in the other. (Thus $Z^2_{(1)}$ is precisely $Z^2$.) Let…
We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
Classical bond percolation theory studies the conditions for a given point in a random graph to be connected to infinity, or "escape" to infinity, via a sequence of random edges. In this work, we present a higher-dimensional generalization…
We consider the set of points visited by the random walk on the discrete torus $(\mathbb{Z}/N\mathbb{Z})^d$, for $d \geq 3$, at times of order $uN^d$, for a parameter $u>0$ in the large-$N$ limit. We prove that the vacant set left by the…
The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and…
We prove that the critical percolation parameter for Finitary Random Interlacements (FRI) is continuous with respect to the path length parameter $T$. The proof uses a result which is interesting on its own right; equality of natural…
We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension: the dynamical exponent is infinite and,…
Let $X_1$, $X_2$, $...$ be a sequence of independently and identically distributed random variables with $\mathsf{E}X_1=0$, and let $S_0=0$ and $S_t=S_{t-1}+X_t$, $t=1,2,...$, be a random walk. Denote $\tau={cases}\inf\{t>1: S_t\leq0\},…
Quantum criticality in the presence of strong quenched randomness remains a challenging topic in modern condensed matter theory. We show that the topology and anomaly associated with average symmetry can be used to predict certain…
We explore the nonunitary dynamics of $(2+1)$-dimensional free fermions and show that the obtained steady state is critical regardless the strength of the nonunitary evolution. Numerical results indicate that the entanglement entropy has a…
We consider $M \geq 2$ pure or random quantum Ising chains of $N$ spins when they are coupled via a single star junction at their origins or when they are coupled via two star junctions at the their two ends leading to the watermelon…
For each $n, d \in \mathbb{N}$ and $0 < \alpha < 1$, we define a random subset of $\mathcal{A}^{\{1, 2, \dots, n\}^d}$ by independently including each element with probability $\alpha$ and excluding it with probability $1-\alpha$, and…
We examine the ground state of the random quantum Ising model in a transverse field using a generalization of the Ma-Dasgupta-Hu renormalization group (RG) scheme. For spatial dimensionality d=2, we find that at strong randomness the RG…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the…
Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay…
Let $\phi(x) = |1 - \frac 1x|$ for all $x > 0$. Then we extend $\phi(x)$ in the usual way to become a continuous map from the compact topological (but not metric) space $[0, \infty]$ onto itself which also maps the set of irrational points…
Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ell$ separated by a distance $r=\alpha\ell$ and quantify their entanglement…