A la recherche de la démonstration perdue de Bienaymé
Nous publions et commentons brièvement une démonstration du théorème critique des processus de branchement très vraisemblablement due à Bienaymé.
A large deviation result for the subcritical Bernoulli percolation
A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices
A large Wiener sausage from crumbs.
A lattice gas model for the incompressible Navier–Stokes equation
We recover the Navier–Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier–Stokes equation in a fixed time interval. The proof does not use nongradient methods or the multi-scale analysis due to the long range jumps.
A Law of the Iterated Logarithm for a Class of Polynomial Hypergroups.
A law of the iterated logarithm for general lacunary series
We prove a law of the iterated logarithm for sums of the form where the satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.
A law of the iterated logarithm for the sample covariance matrix.
A Lemma on Proximity of Variances and Expectations
We define a notion of delta-variance maximization and show it implies epsilon-proximity in expactations.
A lemma on proximity of variances and expectations
A limit law for random walk in a random environment
A limit law for the root value of minimax trees.
A limit theorem for functionals of a Poisson process
A limit theorem for joint distribution of order-statistics from stationary Gaussian sequences
A limit theorem for maxima of nonstationary Gaussian sequences
A limit theorem for the moment of self-normalized sums.
A limit theorem for the position of a particle in the Lorentz model.
A limit theorem for the prediction process under absolute continuity
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A limit theorem for the Riemann zeta-function in the complex space