We study the non equilibrium dynamics of FA-1f (in dimension 1) started from a configuration entirely occupied on the left half-line and focus on the evolution of the front, namely the position of the leftmost zero. KCM are non attractive interacting particle systems and the study of shapes can be complicated. The Friedrickson-Andersen one facilitated spin (FA-1f) model is a kinetically contrained model (KCM) where each spin can flip provided at least one nearest neighbor is empty. So do its excursions above past minima, who then encode measure-changed α-stable trees, in which we make a random number of vertex-identifications to obtain the limit components of the graph.įront of the Friedrickson-Andersen one facilitated spin To this purpose, we run through the graph in a depth-first manner, sampling an exploration process whose limit in law is absolutely continuous with respect to that of a spectrally positive α-stable L\'vy process. degrees, whose law has a power-tail behaviour with exponent α 1 for some α in (1,2), has a metric space scaling limit. We prove that a critical configuration model with i.i.d. Scaling limit of a configuration model with power-law degrees Moreover, we also study critical behavior of this model. In this talk, we prove the limit theorems for random regular graphs with degree larger than 2. In a recent paper, Giardina, Giberti, Hofstad, Prioriello have proved a law of large numbers and a central limit theorem with respect to annealed measure of Ising model on some random graphs including random regular graph of degree 2. aggregation, spread of information and forest-fires.Īnnealed Ising model on random regular graphs Although the study of these properties is interesting in itself, the main motivation comes from questions concerning quite natural processes, e.g. It turns out that certain choices of the various parameters in this model give rise to delicate competing effects on the `global’ connectivity properties of the remaining network. We focus on the case of the triangular lattice. Now suppose that in addition we also remove for each vertex (again independently of the others) with very small probability a (possibly very large) random box centered at the vertex. In the ordinary site percolation model with parameter p, the vertices of a lattice are, independently of each other, removed with probability 1-p. Near-critical percolation with `heavy-tailed’ impurities ![]() Proofs are based on a mixture of ergodic theory and concentration inequalities suited to the “cooling” model. asymptotic speed, large deviations for the empirical speed and fluctuations under recurrence assumptions depending on how fast the resampling occurs. In our interpolating “cooling” model, the random environment is resampled along an increasing sequence of deterministic times and we look at different resampling growing regimes. transient regime with zero speed, polynomial decay of rare events, non-diffusive fluctuations). While in setting (I) strong trapping phenomena are responsible for anomalous limiting behaviors (such as e.g. It is well known that in setting (II) strong homogenization takes place and the asymptotic behavior of the walk is as for an homogeneous Markov chain. We propose a model of a one-dimensional random walk in dynamic random environment that interpolates betweentwo classical settings: (I) the random environment is sampled at time zero only and stays “frozen” (II) the random environment is resampled at every unit of time. Random Walks in Cooling Random Environment We cordially invite you to attend this special afternoon. On Friday afternoon, June 1, there will be a celebration of the extension of the CNRS label UMI that is awarded to Eurandom. ![]() – Daniel Valesin (University of Groningen) Special Afternoon – Irène Marcovici (Université de Lorraine) ![]() – Frank den Hollander (Leiden University) – Aurélia Deshayes (Université Paris Diderot) There will be talks from invited speakers, in and around the mini-course areas Currently confirmed speakers are The conference will contain two mini-courses of The meeting is co-organized within the stochastic groups of TU Eindhoven and Université Paris-Est Créteil within their common CNRS affiliation, and intend to be the occasion to advert and celebrate the renewal of the CNRS-UMI affiliation of Eurandom.Īrnaud Le Ny (CNRS UPEC Paris Est) Speakers The model of the workshop will be the Young European Probalilists series (YEP) that are held annually in Eurandom, consisting of mini-courses and regular talks from both “junior” or “senior” researchers from the Dutch and French probabililist communities. ![]() “Mathematical Statistical Mechanics, Random Graphs and Related Topics” Sponsored byĪléa-Networks-Eurandom fellowships for the Franco-Dutch YEP
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