Noticias en español
The speed of invasion on an advancing population.
Abstract: We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional coupled F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. In that paper, it was noted that the speed of invasion by the mutant trait is faster faster when the resident population ist expanding in space compared to the speed when the resident population is already present everywhere. We use probabilistic methods, in particular the Feynman-Kac...
Read MoreSolution of the polynuclear growth model.
Abstract: The polynuclear growth model (PNG) is a model for crystal growth in one dimension. It is one of the most basic models in the KPZ universality class, and in the droplet geometry, it can be recast in terms of a Poissonized version of the longest increasing subsequence problem for a uniformly random permutation. In this talk, we will show how the multipoint distributions of the model can be expressed through solutions of a classical integrable system, the two-dimensional non-Abelian Toda lattice. In the appropriate scaling limit, these solutions become solutions of the KP equation,...
Read MoreCompetition processes on hyperbolic non-amenable graphs.
Abstract: We consider two first-passage percolation processes, FPP_1 and FPP_\lambda, spreading with rates 1 and \lambda respectively, on a graph G with bounded degree. FPP_1 starts from a single source, while the initial configuration of FPP_\lambda consists of countably many seeds distributed according to a product of iid Bernoulli random variables of parameter \mu on the set of vertices. This model is known as “First passage percolation in a hostile environment” (FPPHE), it was introduced by Stauffer and Sidoravicius as an auxiliary model for investigating a notoriously...
Read MoreQuantitative hydrodynamic limit and regularity for Langevin dynamics for gradient interface models.
Abstract: Lanngevin dynamics for gradient interface models are important in statistical physics due to their connection with random surfaces. It is of particular interest to understand their behavior over large-scales. In this direction a number of results have been established in the last 20 years (including the hydrodynamic limit of Funaki-Spohn and the scaling limit of Naddaf-Spencer and Giacomin-Olla-Spohn). In this talk, we will present the model, its motivations and main results. We will study a connection with the stochastic homogenization of nonlinear equations, discuss some...
Read MoreTail bounds for detection times in mobile hyperbolic graphs.
Abstract: Motivated by Krioukov et al.’s model of random hyperbolic graphs for real-world networks, and inspired by the analysis of a dynamic model of graphs in Euclidean space by Peres et al., we introduce a dynamic model of hyperbolic graphs in which vertices are allowed to move according to a Brownian motion maintaining the distribution of vertices in hyperbolic space invariant. For different parameters of the speed of angular and radial motion, we analyze tail bounds for detection times of a fixed target and obtain a complete picture, for very different regimes, of how and when the...
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