Rigid advection, where a spatial field shifts at constant velocity, provides a convenient baseline for spatio-temporal modeling, but its assumption of perfect correlation along the propagation path is unrealistic for most physical systems. This talk presents a unified perspective on transport modeling, addressing both simulation and estimation.

For simulation, we develop models that relax the rigid structure of simple advection by allowing richer velocity structures, from superpositions of different velocities to spatially varying velocity fields. These generalizations connect naturally to transport-diffusion dynamics and support nowcasting applications.

For estimation, we consider the problem of recovering latent velocity fields from evolving images. Using Gaussian processes with flow-based covariance structures, we produce smooth, spatially complete wind estimates from satellite imagery where standard algorithms struggle.

Por anunciar

Por anunciar

Por anunciar

An asymmetric random variable $X$ is said to be symmetrization resistant if every independent random variable $Y$ that produces a symmetric sum $X+Y$ has a greater variance than that of $X$. Asymmetric Bernoulli random variables were shown to be symmetrization resistant by Kagan, Mallows, Shepp, Vanderbei, and Vardi (1999); Pal (2008) gave a proof using stochastic calculus. Proving symmetrization resistance appears to be difficult: little is known about other asymmetric distributions. We introduce the notion of entropic symmetrization resistance, which is the same as symmetrization resistance except that the entropy (rather than variance) of $Y$ must exceed that of $X$. We show that Bernoulli random variables exhibit entropic symmetrization resistance exactly when they exhibit symmetrization resistance. We also extend the underlying entropy and variance inequalities to the hypercube. Finally, we explore the possibility of extensions to non-Bernoulli random variables. This talk is based on joint work with Mokshay Madiman (University of Delaware).

Activated random walk (ARW) is an ‘abelian’ particle system that conjecturally exhibits the complex behaviors associated with self-organized criticality (SOC), a phenomenon that was first described heuristically by physicists in the 1990s. I will discuss recent results for ARW on Z which rigorously establish some of the predictions of SOC, including universality of the phase transition, and properties of the critical state.