Related papers: Cutoff for the East process
We consider an exclusion process representing a reactive dynamics of a pulled front on the integer lattice, describing the dynamics of first class $X$ particles moving as a simple symmetric exclusion process, and static second class $Y$…
In this paper, we study an approximation scheme for L\'evy processes with drift in terms of a representation that is akin to the celebrated Mehler formula for L\'evy-Ornstein-Uhlenbeck processes. The approximation scheme is based on a…
In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…
We study the nature of the glass transition by cooling model atomistic glass formers at constant rate from a temperature above the onset of glassy dynamics to $T=0$. Motivated by the East model, a kinetically constrained lattice model with…
Because of the negative inclination of the solid-liquid phase separation line in water, ice Ih melts on compression. On further increase in pressure the liquid water transforms into a high density metastable glassy state, characterized by a…
We introduce a new framework for analyzing Glauber dynamics for the Ising model. The traditional approach for obtaining sharp mixing results has been to appeal to estimates on spatial properties of the stationary measure from within a…
We study a class of models for brittle fracture: elastic theory models which allow for cracks but not for plastic flow. We show that these models exhibit, at all finite temperatures, a transition to fracture under applied load similar to…
We introduce a three-dimensional lattice gas model to study the glass transition. In this model the interactions come from the excluded volume and particles have five arms with an asymmetrical shape, which results in geometric frustration…
In this paper, we follow in the footsteps of Onsager and Machlup (OM) and consider diffusion-like paths that are explored by a particle moving via a conservative force while being in thermal equilibrium with its surroundings. Instead of…
The canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cut-off in the interaction range. The sharp cut-off renders the potential non-analytic, but makes it…
Consider a uniform rooted Cayley tree $T_{n}$ with $n$ vertices and let $m$ cars arrive sequentially, independently, and uniformly on its vertices. Each car tries to park on its arrival node, and if the spot is already occupied, it drives…
Given a sequence $(\mathfrak{X}_i, \mathscr{K}_i)_{i=1}^\infty$ of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lower order than the mixing time. We study mixing times and…
We study the effect of a small cutoff $\epsilon$ on the velocity of a pulled front in one dimension by means of a variational principle. We obtain a lower bound on the speed dependent on the cutoff, and for which the two leading order terms…
We consider the multicolour East model, a model of glass forming liquids closely related to the East model on $\mathbb{Z}^d$. The state space ${(G\cup \{\star\})}^{\mathbb{Z}^d}$ consists of $|G|\le 2^d$ different vacancy types and the…
Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory and holography. We tackle this problem in 1D…
In 1975 Edwards and Anderson introduced a new paradigm that interacting quenched systems, such as a spin-glass, have a phase transition in which long time memory of spatial patterns is realized without spatial correlations. We show here…
We consider the following Markovian dynamic on point processes: at constant rate and with equal probability, either the rightmost atom of the current configuration is removed, or a new atom is added at a random distance from the rightmost…
Quantum measurement is a physical process. A system and an apparatus interact for a certain time period (measurement time), and during this interaction, information about an observable is transferred from the system to the apparatus. In…
The mode-coupling theory for ideal glass transitions in simple systems is generalized to a theory for the glassy dynamics of molecular liquids using the density fluctuations of the sites of the molecule's constituent atoms as the basic…
We consider the dynamics of particle systems where the particles are confined by impenetrable barriers to a bounded, possibly non-convex domain $\Omega$. When particles hit the boundary, we consider an instant change in velocity, which…