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For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller-Markov property (with respect to the space variable) at some time is conserved at later times, and an evolution equation is derived for the infini-tesimal generator. Previously known explicit solutions… (More)

We introduce order parameter models for describing the dynamics of sand ripple patterns under oscillatory flow. A crucial ingredient of these models is the mass transport between adjacent ripples, which we obtain from detailed numerical simulations for a range of ripple sizes. Using this mass transport function, our models predict the existence of a stable… (More)

In this paper, we investigate the theoretical guarantees of penalized ℓ 1-minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with non-necessarily random noise, when the sensing operator belongs to the Gaussian ensemble (i.e. random design matrix with i.i.d.… (More)

We consider Burgers equation forced by a brownian in space and white noise in time process ∂tu + 1 2 ∂x(u) 2 = f (x, t), with E(f (x, t)f (y, s)) = 1 2 (|x| + |y| − |x − y|)δ(t − s) and we show that there are Levy processes solutions, for which we give the evolution equation of the characteristic exponent. In particular we give the explicit solution in the… (More)

We compute the small-tau expansion up to the third order for the form factor of two glued quantum star graphs with Neumann boundary conditions, by taking into account only the most backscattering orbits. We thus show that the glueing has no effect if the number of glueing edges is negligible compared to the number of edges of the graph, whereas it has an… (More)

We compute the three point correlation function for the eigenvalues of the Laplacian on quantum star graphs in the limit where the number of edges tends to infinity. This extends a work by Berkolaiko and Keating, where they get the 2-point correlation function and show that it follows neither Poisson, nor random matrix statistics. It makes use of the trace… (More)

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