Related papers: Structure and diffusion time scales of disordered …
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and…
The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using…
We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of…
Let $\mathcal{T}$ be a supercritical Galton-Watson tree with a bounded offspring distribution that has mean $\mu >1$, conditioned to survive. Let $\varphi_{\mathcal{T}}$ be a random embedding of $\mathcal{T}$ into $\mathbb{Z}^d$ according…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented…
We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…
I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
We characterize the early stages of the approach to equilibrium in isolated quantum systems through the evolution of the entanglement spectrum. We find that the entanglement spectrum of a subsystem evolves with at least three distinct…
Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper…
We consider critical site percolation ($p=p_c=1/2$) on the triangular lattice $\mathbf{T}$ in two dimensions. We show that the simple random walk on the clusters of open vertices converges in the scaling limit to a continuous diffusion…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
Propagation of ultrashort light pulses in disordered multilayers is studied by using numerical simulations in time domain. We consider cases of instantaneous and noninstantaneous Kerr nonlinearities of the structure materials. The…
The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the…
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…