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Conformal weldings of random surfaces: SLE and the quantum gravity zipper
Conformal weldings of random surfaces: quantum gravity zipper
2011/2/24
We construct a conformal welding of two Liouville quantum gravity random surfaces and show that the interface between them is a random fractal curve called the Schramm-Loewner evolution (SLE), thereby...
Connectivity properties of random interlacement and intersection of random walks
Random interlacement random walk intersection of random walks capacity
2011/2/24
We consider the interlacement Poisson point process on the space of doubly-infinite Zd-valued
trajectories modulo time shift, tending to infinity at positive and negative infinite times. The set of v...
On the speed of biased random walk in translation invariant percolation
speed of biased random translation invariant percolation
2011/2/21
For biased random walk on the infinite cluster in supercritical i.i.d.percolation on Z2, where the bias of the walk is quantified by a parameter > 1,it has been conjectured (and partly proved) that ...
Distributed Detection over Random Networks: Large Deviations Performance Analysis
Chernoff information distributed detection random network running consensus
2011/2/24
We study the large deviations performance, i.e., the exponential decay rate of the error probability, of distributed detection algorithms over random networks.
Giant vacant component left by a random walk in a random d-regular graph
Random walk vacant set regular graph expanders random interlacement
2011/2/25
We study the trajectory of a simple random walk on a d-regular graph with d ≥ 3 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular grap...
From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics
fractional Brownian motion stochastic integrals rough paths
2011/2/22
Let B = (B1(t), . . . ,Bd(t)) be a d-dimensional fractional Brownian motion with Hurst index ≤ 1/4, or more generally a Gaussian process whose paths have the same local regularity. Defining properly...
Lamplighter Random Walks and Entropy-Sensitivity of Languages
Lamplighter Random Walks Entropy-Sensitivity of Languages
2011/1/21
I declare that I have authored this thesis independently, that I have not used other than the declared sources/resources, and that I have explicitely marked all material which has been quotes either l...
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotyp...
Foliated stochastic calculus: Harmonic measures
Foliation diffusion process stochastic calculus
2011/2/24
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foli-ation.
Localization for equivariant cohomology with varying polarization
equivariant cohomology Hamiltonian G-spaces equivariant localization proper cobordism
2011/2/22
We develop a localization theorem in equivariant cohomology that generalizes both the localization with respect to a component of the momentum map and the localization with respect
to the norm square...
Hitting distributions of simple random walks on Sierpinski graphs
In [Ka] Kaimanovich de ned an augmented rooted tree X for the
2011/2/25
In [Ka], Kaimanovich de ned an augmented rooted tree X for the d-dimensional Sierpinski gasket K. Let fZtg be the simple random walk on X,starting at the root ;.
Wegner estimate and Anderson localization for random magnetic fields
Wegner estimate Anderson localization random Schr¨odinger operator
2011/2/25
We consider a two dimensional magnetic Schr¨odinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier mod...
Information-Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements
Information-Theoretic Capacity Error Exponents of Stationary Point Processes
2011/2/25
This paper studies the Shannon regime for the random displacement of stationary point processes. Let each point of some initial stationary point process in Rn give rise to one daughter point, the loca...
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood.We provide conditions under which the pertur...
Positive Lyapunov exponent by a random perturbation
Lyapunov exponent random perturbation
2010/12/28
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood.We provide conditions under which the pertur...