All Questions

It seems the KPZ is the next big thing in mathematical physics and probability. The skeletal idea is probably that while classical averages are in the Gaussian universality class, lots of other ...

What kind of approaches can be used to study the following quasilinear parabolic pde for a scalar function $u=u(x,t)$ ? $$ u_t= u \ u_{x x} $$ The physical problem where this pde comes from dictates ...

Thanks to the work by M. Yor and colleagues, much is known about the following exponential of Brownian motion: $X= \int_0^{\infty}{\rm d}t \ e^{-t + g \ B(t)}$ where $g$ is a real scale parameter. ...

Here exponentially localized can be thought in a non-rigorous manner as a measure that is mostly supported on a sparse number of nodes. Some intuition can gained by thinking about a diffusion process, ...

Consider a system of interacting non-linear oscillators governed by the McKean-Vlasov equation: $$\frac{\partial p(x,t)}{\partial t} = \frac{\partial}{\partial x}\left[\frac{\partial V(x)}{\partial x}...