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Single--crossover recombination and ancestral recombination trees
population genetics recombination segmentation process ancestral trees
2012/6/21
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the...
On the length of one-dimensional reactive paths
one-dimensional reactive paths Probability
2012/6/21
Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simplecsetting, namely paths generated by a one-dimensional overdamped Langevin...
Moderate deviations for random field Curie-Weiss models
Random field Curie-Weiss model disordered mean-field moderate deviations large deviations transfer principle
2012/6/21
The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interes...
Weights and degrees in a random graph model based on 3-interactions
Martingale random graph preferential attachment scale-free property
2012/6/19
In a random graph model based on 3-interactions we give the joint asymptotic distribution of weights and degrees and prove scale-free property for the model. Moreover, we determine the asymptotics of ...
From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields
Gaussian processes Hausdorff dimension (multi)fractional Brownian motion multiparameter processes Holder regularity stationarity
2012/6/19
Fine regularity of stochastic processes is usually measured in a local way by local H\"older exponents and in a global way by fractal dimensions. Following a previous work of Adler, we connect these t...
Log-Harnack Inequality for Gruschin Type Semigroups
Gruschin semigroup log-Harnack inequality coupling regular conditional probability
2012/6/19
By constructing a coupling in two steps and using the Girsanov theorem under a regular conditional probability, the log-Harnack inequality is established for a large class of Gruschin type semigroups ...
Central limit theorem for partial linear eigenvalue statistics of Wigner matrices
Central limit theorem partial linear eigenvalue statistics Wigner matrices Probability
2012/6/19
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered e...
The Wronskian parameterizes the class of diffusions with a given distribution at a random time
class of diffusions distribution random time Probability
2012/6/19
We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion...
Cover times for sequences of Markov chains on random graphs
Random walk Cover time Maximal hitting time Random graph
2012/6/15
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (type 1) is the class of cover times approximated by the maximal hitting times s...
Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields
Gaussian random determinant Wishart matrix Gaussian random parallelotope mixed volumes of ellipsoids location-dispersion ellipsoid
2012/6/15
Consider a $d\times d$ matrix $M$ whose rows are independent centered non-degenerate Gaussian vectors $\xi_1,...,\xi_d$ with covariance matrices $\Sigma_1,...,\Sigma_d$. Denote by $\mathcal{E}_i$ the ...
Extreme values for two-dimensional discrete Gaussian free field
Extreme values two-dimensional discrete Gaussian free field Probability
2012/6/15
We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry...
Semi-infinite paths of the 2d-Radial Spanning Tree
stochastic geometry random tree semi-infinite path asymptotic direction competition interface
2012/6/9
We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite pa...
An Inhomogeneous Multispecies TASEP on a Ring
Inhomogeneous Multispecies TASEP Ring Probability
2012/6/14
We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the ...
This text is a survey (Bourbaki seminar) on the paper "Liouville quantum gravity and KPZ" By B.Duplantier and S.Sheffield.
Nonconventional Large Deviations Theorems
large deviations Markov processes nonconventional averages hyperbolic diffeomorphisms
2012/6/12
We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hy...