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Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high ord...
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar steepest descent method and double scaling limit, we obtain Painleve asymptotics in two transitio...
We prove the existence and give the asymptotic behavior of non local fronts in homogeneous media.
In this paper we initiate a quantitative theory of trace characters  of reductive p-adic groups when the representation  varies. Our approach is based on the local constancy of characters and we su...
The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It can be used to definea deterministic aggregation model analogous to internal diffusion limited aggregation. ...
The rotor-router model is a deterministic analogue of random walk.It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a...
Mathematical tools are developed for describing low-dimensional projec- tions of high-dimensional data. Theorems are given to show that under suitable conditions, most projections are approximatel...
In this paper we consider the motion of a tracer in a flow that is locally self-similar and whose correlations decay at infinity but at the rate that does not guarantee that the flow does not have ”me...
We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying, then ...
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-...
We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed o...
In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness conditions on the re...
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering f...

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