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We are delighted to organize and host the second edition of the biennial Summer School on Random Matrices at the University of Michigan during June 18--29, 2018.We thank the Michigan Center for Applie...
We study the homogenization of an obstacle problem in a perforated domain, when the holes are periodically distributed and have random shape and size. The main assumption concerns the capacity of the ...
Homogenization of a Hele-Shaw problem in periodic and random media
Free boundary problem Hele-Shaw equation Obstacle problem Viscosity solution Homogenization
2015/10/15
We investigate the homogenization limit of a free boundary problem with space-dependent free boundaryvelocities. The problem under consideration has a well-known obstacle problem transformation, forma...
Random Iteration of Maps on a Cylinder and diffusive behavior
Random Iteration of Maps Cylinder diffusive
2015/9/25
Random Iteration of Maps on a Cylinder and diffusive behavior.
FAST METHOD FOR HIGH-FREQUENCY ACOUSTIC SCATTERING FROM RANDOM SCATTERERS
acoustic scattering random domains uncertainty quantification boundary integral equations fast algorithms quasi–Monte Carlo methods
2015/7/14
This paper is concerned with the uncertainty quantification of high-frequency acoustic scattering from objects with random shape in two-dimensional space. Several new methods are introduced to efficie...
Time splitting for wave equations in random media
Time splitting wave equations random media
2015/7/14
Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and sp...
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The ...
Time splitting for the Liouville equation in a random medium
Time splitting Liouville equation random medium
2015/7/14
We consider the Liouville equations with highly heterogeneous Hamiltonians and their numerical solution by a time splitting algorithm. Such equations model the density of particles evolving according ...
Passive tracer in a slowly decorrelating random flow with a large mean
Passive tracer slowly decorrelating random flow large mean
2015/7/14
We consider the movement of a particle advected by a random flow of the form v + δF(x), with v ∈ Rd a constant drift, F(x) – the fluctuation – given by a zero mean, stationary random field and δ 1 s...
Wave field correlations in weakly mismatched random media
Wave field correlations weakly mismatched random media
2015/7/14
This paper concerns the derivation of a Fokker-Planck equation for the correlation of two high frequency wave fields propagating in two different random media. The mismatch between therandom media nee...
This paper reviews several mathematical techniques that have been developed to analyze the asymptotic behavior of waves and particles propagating in a heterogeneous medium. The heterogeneous medium is...
Waves in weakly random media:lecture notes for the Vienna Inverse Problems school
weakly random media Vienna Inverse Problems
2015/7/14
Wave propagation in complex media is an ubiquitous phenomenon–applications include light propagation through the atmosphere, underwater acoustic, tomography, and innumerable other ones. These problems...
Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems
Random Quadratic Systems Solving Linear Systems
2015/6/17
We consider the fundamental problem of solving quadratic systems of equations in n variables, where yi = |hai, xi|2, i = 1, . . . , m and x ∈ Rn is unknown. We propose a novel method, which starting w...
Heavy Random Truncation
Heavy Random Truncation
2015/3/20
Consider an infinite sequence of independent random vectors (Xm, Ym), m = 1, 2, · · · ,where the X m have a common distribution function F and the Ym
have a common distribution function G. The compon...
Asymptotics of the Fredholm determinant corresponding to the first bulk critical universality class in random matrix models
Integrable operators Riemann-Hilbert approach Deift-Zhou method asymptotical analysis of Fredholm determinants
2015/1/19
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...