Abstract: An invariance principle for Azéma martingales is presented as well as a new device to construct solutions of Emery’s structure equations. 1.

We prove an almost sure invariance principle for diffusion driven by velocities with unbounded stationary vector potentials. The result generalizes to multiple particles motion, driven by a common velocity field and independent molecular Brownian motions.

The non-linear invariance principle of Mossel, O’Donnell and Oleszkiewicz establishes that if fpx1,..., xnq is a multilinear low-degree polynomial with low influences then the distribution of fpB1,...,Bnq is close (in various senses) to the distribution of fpG1,...,Gnq, where Bi PR t´1, 1u

In this paper we address the problem of extending La Salle Invariance Principle to switched system. We prove an extension of the invariance principle relative to dwell-time switched solutions, and a second one relative to constrained switched systems.

Abstract. We prove invariance principles for phase separation lines in the two dimensional nearest neighbour Ising model up to the critical temperature and for connectivity lines in the general context of high temperature finite range ferro-magnetic Ising models. Nous prouvons des principes d’invariance

We show a new invariance principle for the radius and other functionals of a class of conditioned ‘Boltzmann-Gibbs’distributed random planar maps. It improves over the more restrictive case of bipartite maps that was discussed in Marckert and Miermont (2006). As in the latter paper, we make use

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Consider the nonlinear mapping F (y) = y ) + u 2 (y) u 0 (y; y ) acting from H 2 into H, where the Hilbert space H = fq : q 2 L (T); q(x)dx = 0g and H 2 = fy; y 2 Hg. Here the functions u 1 ; u 2 are real analytic and and u 2 (y) 6 0: the constant u 0 is such that F (y) 2 H. We prove that the map F is a real analytic isomorphism and a priori two-sided estimates of norms of F (y); y are obtaned. We apply these results to the inverse problems for the Schrodinger operators 2 + q(x) in L (R) with a 1-periodic potential. In particular we use this result to study the Camassa-Holm equation.

We consider Galton-Watson trees associated with a critical offspring distribution and conditioned to have exactly n vertices. These trees are embedded in the real line by affecting spatial positions to the vertices, in such a way that the increments of the spatial positions along edges of the tree are independent variables distributed according to a symmetric probability distribution on the real line. We then condition on the event that all spatial positions are nonnegative. Under suitable assumptions on the offspring distribution and the spatial displacements, we prove that these conditioned spatial trees converge as n → ∞, modulo an appropriate rescaling, towards the conditioned Brownian tree that was studied in previous work. Applications are given to asymptotics for random quadrangulations. 1

Abstract not found