Related papers: Factorised Steady States in Mass Transport Models …
We consider a decentralised multi-access algorithm, motivated primarily by the control of transmissions in a wireless network. For a finite single-hop network with arbitrary interference constraints we prove stochastic stability under the…
We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for…
Selecting regularization parameters in penalized high-dimensional graphical models in a principled, data-driven, and computationally efficient manner continues to be one of the key challenges in high-dimensional statistics. We present…
We analyze pattern formation on a network of cells where each cell inhibits its neighbors through cell-to-cell contact signaling. The network is modeled as an interconnection of identical dynamical subsystems each of which represents the…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
We characterize steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume $L^d$, where both mass and {\it center-of-mass} (CoM) remain conserved and detailed balance…
Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…
We consider the transport statistics of classical bistable systems driven by noise. The stochastic path integral formalism is used to investigate the dynamics and distribution of transmitted charge. Switching rates between the two stable…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
We numerically survey predictions on the shapes and scaling laws of particle condensates that emerge as a result of spontaneous symmetry breaking in pair- factorized steady states of a stochastic transport process. The specific model…
Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…
With the help of Monte Carlo simulations and a mean-field theory, we investigate the ordered steady-state structures resulting from the motion of a single vacancy on a periodic lattice which is filled with two species of oppositely…
We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
We carry out a delay stability analysis (i.e., determine conditions under which expected steady-state delays at a queue are finite) for a simple 3-queue system operated under the Max-Weight scheduling policy, for the case where one of the…
We study criteria which ensure that Gibbs states (often also called generalized vacuum states) on distance-regular graphs are positive. Our main criterion assumes that the graph can be embedded into a growing family of distance-regular…
We propose a framework for constructing microscopic traffic models from microscopic acceleration patterns that can in principle be experimental measured and proper averaged. The exact model thus obtained can be used to justify the…
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…