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Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is…
For a given dimension d $\ge$ 2 and a finite measure $\nu$ on (0, +$\infty$), we consider $\xi$ a Poisson point process on R d x (0, +$\infty$) with intensity measure dc $\otimes$ $\nu$ where dc denotes the Lebesgue measure on R d. We…
We calculate the time dependent nonequilibrium current through a single level quantum dot strongly coupled to a vibrational mode. The nonequilibrium real time dynamics caused by an instantaneous coupling of the leads to the quantum dot is…
The main purpose of this paper is to introduce and establish basic results of a natural extension of the classical Boolean percolation model (also known as the Gilbert disc model). We replace the balls of that model by a positive…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
We explore the free boson unitary dynamics subject to repeated random forced measurement. The input state is chosen as a Fock state in real space with the particle number conserved in the entire dynamics. We show that each boson is…
We study a lattice model where the coupling stochastically switches between repulsive (subtractive) and attractive (additive) at each site with probability p at every time instance. We observe that such kind of coupling stabilizes the local…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…
In this paper we study the Poisson stick model in two dimensional hyperbolic space $\mathbb{H}^2,$ where the sticks all have length $L.$ Typically, percolation models in hyperbolic space undergo two phase transitions as the intensity…
Bootstrap percolation is a prominent framework for studying the spreading of activity on a graph. We begin with an initial set of active vertices. The process then proceeds in rounds, and further vertices become active as soon as they have…
We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…
We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. Stationary cocycles are constructed for…
Quantum simulation in its current state faces experimental overhead in terms of physical space and cooling. We propose boson sampling as an alternative compact synthetic platform performing at room temperature. Identifying the capability of…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
We prove the absence of percolation in a directed Poisson-based random geometric graph with out-degree $1$. This graph is an anisotropic variant of a line-segment based lilypond model obtained from an asymmetric growth protocol, which has…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…