-
作者：Broutin, Nicolas; Marckert, Jean-Francois
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux
摘要：We revisit the discrete additive and multiplicative coalescents, starting with n particles with unit mass. These cases are known to be related to some combinatorial coalescent processes: a time reversal of a fragmentation of Cayley trees or a parking scheme in the additive case, and the random graph process in the multiplicative case. Time being fixed, encoding these combinatorial objects in real-valued processes indexed by the line is the key to describing the asymptotic behaviour of the mass...
-
作者：Brunel, Victor-Emmanuel
作者单位：Institut Polytechnique de Paris; ENSAE Paris; University of Haifa
摘要：We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in R-d. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension d, unlike the other estimators that have been proposed so far. For d >= 3, our estimator has a better risk than the previous ones, and it is nearly minimax, up to a logarithmic factor. We also propose an estimator which is adaptive with respect to the structure ...
-
作者：Delarue, Francois; Diel, Roland
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional stochastic differential equations, the drift of which is a distribution, by means of rough paths theory. Existence and uniqueness are established in the weak sense when the drift reads as the derivative of a -Holder continuous function, . Regularity of the ...
-
作者：Nicolaescu, Liviu I.
作者单位：University of Notre Dame
摘要：We prove that a Gaussian ensemble of smooth random sections of a real vector bundle over compact manifold canonically defines a metric on together with a connection compatible with it. Additionally, we prove a refined Gauss-Bonnet theorem stating that if the bundle and the manifold are oriented, then the Euler form of the above connection can be identified, as a current, with the expectation of the random current defined by the zero-locus of a random section in the above Gaussian ensemble.
-
作者：Lee, Ji Oon; Schnelli, Kevin
作者单位：Korea Advanced Institute of Science & Technology (KAIST); Institute of Science & Technology - Austria
摘要：We consider random matrices of the form H = W + lambda V, lambda is an element of R+, where W is a real symmetric or complex Hermitian Wigner matrix of size N and V is a real bounded diagonal random matrix of size N with i. i. d. entries that are independent of W. We assume subexponential decay of the distribution of the matrix entries of W and we choose lambda similar to 1, so that the eigenvalues of W and lambda V are typically of the same order. Further, we assume that the density of the en...
-
作者：Gu, Yu; Mourrat, Jean-Christophe
作者单位：Stanford University; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension 3 and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.
-
作者：Goetze, F.; Tikhomirov, A.
作者单位：University of Bielefeld; Syktyvkar State University; Russian Academy of Sciences; Komi Science Centre of the Ural Branch of the Russian Academy of Sciences
摘要：Let X = (X-jk)(j,k=1)(n) denote a Hermitian random matrix with entries X-jk, which are independent for 1 <= j <= k <= n. We consider the rate of convergence of the empirical spectral distribution function of the matrix X to the semi-circular law assuming that EX (jk) = 0, EXjk2 = 1 and that sup(n >= 1) sup(1 <= j, k <= n) E vertical bar X-jk vertical bar(4) =: mu(4) < infinity, and sup(1 <= j,k <= n) vertical bar X-jk vertical bar <= D(0)n(1/4) By means of a recursion argument it is shown that...
-
作者：Corwin, Ivan; Hammond, Alan
作者单位：Columbia University; Sorbonne Universite; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：For each t >= 1we construct an -indexed ensemble of random continuous curves with three properties: the lowest indexed curve is distributed as the time t Hopf-Cole solution to the Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation with narrow wedge initial data; the entire ensemble satisfies a resampling invariance which we call the -Brownian Gibbs property [with H(x) = e(x)]; increments of the lowest indexed curve, when centered by and scaled down vertically by and horizontall...
-
作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：Any renewal processes on N-0 with a polynomial tail, with exponent a is an element of (0, 1), has a non-trivial scaling limit, known as the alpha-stable regenerative set. In this paper we consider Gibbs transformations of such renewal processes in an i. i. d. random environment, called disordered pinning models. We show that for alpha is an element of (1/2, 1) these models have a universal scaling limit, which we call the continuum disordered pinning model (CDPM). This is a random closed subse...
-
作者：Curien, Nicolas; Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We study the random metric space called the Brownian plane, which is closely related to the Brownian map and is conjectured to be the universal scaling limit of many discrete random lattices such as the uniform infinite planar triangulation. We obtain a number of explicit distributions for the Brownian plane. In particular, we consider, for every , the hull of radius r, which is obtained by filling in the holes in the ball of radius r centered at the root. We introduce a quantity which is inte...
