Noticias en español
Lattice trees in high dimensions.
Resumen: Lattice trees is a probabilistic model for random subtrees of . In this talk we are going to review some previous results about the convergence of lattice trees to the “Super-Brownian motion” in the high-dimensional setting. Then, we are going to show some new theorems which strengthen the topology of said convergence. Finally, if time permits, we will discuss the applications of these results to the study of random walks on lattice trees. Joint work with A. Fribergh, M. Holmes and E. Perkins.
Read MoreExistence of solution and localization for the SHE with multiplicative Lévy white noise.
Resumen: We consider the following stochastic PDE in $$ \partial_t u = \Delta u + \xi \cdot u $$ where $u$ is a function of space and time. The operator $\Delta$ denotes the usual Laplacian in $\mathbb R^d$ and $\xi$ is a space-time Lévy white noise. This equation has been extensively studied in the case where $\xi$ is a Gaussian White noise. In that case, the equation is well-posed only when the space dimension $d$ is equal to one. In our talk, we consider the case where $\xi$ is a Lévy white noise with no diffusive part and only positive jumps. We identify necessary and sufficient...
Read MoreEcuaciones de Burgers acopladas.
Resumen: Las ecuaciones de Burgers acopladas fueron introducidas en los años 90 en el estudio de interfaces aleatorias en física de materiales. Posteriormente, fueron utilizadas, entre otros contextos, como modelos de sedimentación y en magnetohidrodinámica. Matemáticamente, fueron estudiadas por Funaki y coautores desde el punto de vista de las distribuciones paracontroladas y por Gubinelli y Perkowski desde el punto de vista de las soluciones de energía. En este trabajo, introducimos una discretización de estas ecuaciones que se puede entender como un sistema de modelos de Sasamoto-Spohn...
Read MoreApproximation of a cross-diffusion system by repulsive random walks.
Resumen: Cross-diffusion systems are a class of partial differential equations used to describe the diffusion of populations showing local repulsion. In this talk we will consider a stochastic individual-based model evolving on a discrete space and we will show that we can obtain convergence to an object in the former class under suitable scales and conditions. The model takes into account two species, where each one is sensitive to the number of individuals of the other species through the individual rate of motion of the particles, this being proportional to the density of individuals on...
Read MoreNon-intersecting paths in the plane, loop-erased walks and random matrices.
Resumen: Non-intersecting processes in one dimension have long been an integral part of random matrix theory, at least since the pioneering work of F. Dyson in the 1960s. For planar (two-dimensional) state space processes, it is not clear how to generalize these connections since the paths under consideration are allowed to have self-intersections (or loops). In this talk, we address this problem and consider systems of random walks in planar graphs constrained to a certain type of non-intersection involving their loop-erased parts (this is closely related to connectivity probabilities of...
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