Related papers: Stochastic Flips on Dimer Tilings
We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…
We study a directed flipping process that underlies the performance of the random edge simplex algorithm. In this stochastic process, which takes place on a one-dimensional lattice whose sites may be either occupied or vacant, occupied…
We consider dimer models on graphs which are bipartite, periodic and satisfy a geometric condition called {\em isoradiality}, defined in \cite{Kenyon3}. We show that the scaling limit of the height function of any such dimer model is…
This paper introduces an elliptic quasi-variational inequality (QVI) problem class with fractional diffusion of order $s \in (0,1)$, studies existence and uniqueness of solutions and develops a solution algorithm. As the fractional…
In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are…
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or micro-scale particles where rolling is an approximation for strong static friction. We consider the simplest possible…
We study a model of random surfaces arising in the dimer model on the honeycomb lattice. For a fixed ``wire frame'' boundary condition, as the lattice spacing $\epsilon\to0$, Cohn, Kenyon and Propp [CKP] showed the almost sure convergence…
Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…
A \emph{stacked triangulation} of a $d$-simplex $\mathbf{o}=\{1,\ldots,d+1\}$ ($d\geq 2$) is a triangulation obtained by repeatedly subdividing a $d$-simplex into $d+1$ new ones via a new vertex (the case $d=2$ is known as an Appolonian…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
We establish the first polynomial upper bound for the mixing time of random edge flips on rooted quadrangulations: we show that the spectral gap of the edge flip Markov chain on quadrangulations with $n$ faces admits, up to constants, an…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
An edge switch is an operation which makes a local change in a graph while maintaining the degree of every vertex. We introduce a switch move, called a triangle switch, which creates or deletes at least one triangle. Specifically, a make…
We use molecular dynamics simulations to study the driven phases of particles such as vortices or colloids moving over a decagonal quasiperiodic substrate. In the regime where the pinned states have quasicrystalline ordering, the driven…
Self-assembly is the process in which the components of a system, whether molecules, polymers, or macroscopic particles, are organized into ordered structures as a result of local interactions between the components themselves, without…
Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical reaction kinetics and related areas. In this paper an almost…