We explain an exact solution of the one-dimensional
Kardar-Parisi-Zhang equation with sharp wedge initial data.
Physically this solution describes the shape fluctuations of a thin
film droplet formed by the stable phase expanding into the...
The Coulomb Gas is a model of Statistical Mechanics with a
special type of phase transition. In the first part of the talk I
will review the expected features conjectured by physicists and the
few mathematical results so far obtained. The second...
This talk will be a progress report on an ongoing research
project which is joint work with Ajay Chandra and Gianluca Guadagni
and which concerns a p-adic analog of the Brydges-Mitter-Scoppola
phi-4 model with...
Using the spectral multiplicities of the standard torus, we
endow the Laplace eigenspace with Gaussian probability measure.
This induces a notion of a random Gaussian Laplace eigenfunctions
on the torus. We...
For many elegant mathematical examples, one can 1) find theories
behind them, 2) understand why they exist in the first place, 3)
explore the consequences in math and physics. If one takes the
Euler number as...
The Gaussian central limit theorem says that for a wide class of
stochastic systems, the bell curve (Gaussian distribution)
describes the statistics for random fluctuations of important
observables. In this...
We develop the droplet scaling theory for the low temperature
critical behavior of two-dimensional Ising spin glasses. The models
with integer bond energies vs. continuously-distributed bond
energies are in the...
Concentration phenomena for Laplacian eigenfunctions can be
studied by obtaining estimates for their $L^{p}$ growth. By
considering eigenfunctions as quasimodes (approximate
eigenfunctions) within the...
In this talk I will describe a real-variable method to extract
long-time asymptotics for solutions of many nonlinear equations
(including the Schrodinger and mKdV equations). The method has many
resemblances to the classical stationary phase method...
I will discuss the problem of determining the number of
infinite-volume ground states in the Edwards-Anderson (nearest
neighbor) spin glass model on $Z^D$ for $D \geq 2$. There are no
complete results for this problem even in $D=2$. I will focus
on...
