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In the paper [STW], it was shown that “a Brownian motion reflected on an independent time-reversed Brownian motion is again a Brownian motion” combining the fact that the
We will see in Section 4.1 that, assuming the Lifshitz tail effect in [ 12 ] , our result indeed derives the correct upper bound of the quenched asymptotics for the Brownian
Indeed, it seems that case (a) should give us the right picture: in the limit, in between large events lineages perform Brownian motions on the torus of sidelength 1 due to
Key words: Brownian areas, asymptotics for density functions right tail, double Laplace transform, two-dimensional saddle point method.. AMS 2000 Subject Classification:
To prove those results, we use the fact that the ISE has the same distribution (up to a constant scaling) as the total mass of an excursion of the Brownian snake conditioned to have
This result has consequences for the Hausdorff dimension of the frontier of planar Brownian motion, and also for the Hausdorff dimension of the set of cut-points of planar
Hereafter, we exploit the Mellin convolution of generalized Gamma densities in order to write explicitly the solutions to fractional diffusion equations.. The claimed result
An impressive number of examples have by now established the fact that both partial differential and difference equations integrable through spectral methods possess the
