In this talk we shall present the construction of a stochastic process, which is related to the parabolic p-Laplace equation in the same way as Brownian motion is to the classical heat equation given by the (2-) Laplacian.
This is a joint work with Viorel Barbu and Marco Rehmeier.
Nonlocal modeling, analysis and computation: some recent development
Abstrac
Nonlocality has become increasingly prominent in nature, leading to the development of new mathematical theories to model and simulate its impact. In this lecture, we will concentrate on nonlocal models that involve interactions with a finite horizon, examining their significance in understanding phenomena involving potential anomalies, singularities, and other effects that arise from nonlocal interactions. Furthermore, we will present recent analytical studies that explore nonlocal operators and function spaces, discussing how they contribute to the development of robust numerical algorithms.
On three classical beta ensembles on the real line
Abstract
Gaussian beta ensembles, beta Laguerre ensembles and beta Jacobi ensembles are three beta ensembles on the real line associated with the Gaussian weight, the Laguerre weight and the Jacobi weight, respectively. Here the parameter beta is regarded as the inverse temperature of the system. It is noted that these three beta ensembles are now realized as eigenvalues of certain random tridiagonal matrices.
This talk gives a brief introduction to the study of global spectral properties of these ensembles.
Discrete integrable equations can be considered in two, three or N-dimensions, as equations fitted together in a self-consistent way on a square, a cube or an N-dimensional cube. We show to find their symmetry reductions (and other properties) through a geometric perspective.
