Related papers: Attractive nearest-neighbor spin systems on the in…
We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution $p(k)$ can be chosen arbitrarily, but which allows for further fine-tuning of the topology…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
The quantum dynamics of a localized spin-$\frac{1}{2} $ Particle interacting with an absorbing environment is investigated. The quantum Langevin-Schr\"odinger equation for spin-$\frac{1}{2} $ is obtained. The susceptibility function of the…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
We study discrete time Markov processes with periodic or open boundary conditions and with inhomogeneous rates in the bulk. The Markov matrices are given by the inhomogeneous transfer matrices introduced previously to prove the…
Ramsey spectroscopy has become a powerful technique for probing non-equilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to…
We investigate the decoherence of a spin 1/2 subsystem weakly coupled to an environment of many spins 1/2 with and without mutual coupling. The total system is closed, its state is pure and evolves under Schroedinger dynamics. Nevertheless,…
We study the dynamics of entanglement in the one-dimensional spin-1/2 XY model in the presence of a transverse magnetic field. A pair of spins are considered as an open quantum system, while the rest of the chain plays the role of the…
We investigate the formation and transport properties of chiral Andreev edge states in a two-dimensional quantum Hall system proximitized by a superconductor. By numerically modeling the system using the Bogoliubov-de Gennes equations, we…
A 1977 theorem of T. Harris states that an attractive spin system preserves the class of associated probability measures. We study analogues of this result for measures that satisfy various conditional positive correlations properties. In…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…
Motivated by recent findings, we discuss the existence of a direct and robust mechanism providing discontinuous absorbing transitions in short range systems with single species, with no extra symmetries or conservation laws. We consider…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self-organizes into an…
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is…
We solve for the dynamics of a pair of spins, coupled to each other and also to an environmental sea of oscillators. The environment mediates an indirect interaction between the spins, causing both mutual coherence effects and dissipation.…
We examine a system of interacting random walks with leftward drift on $\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become…
In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…