The parabolic Anderson problem is the Cauchy problem for the heat equation âˆ‚tu(t, z) = âˆ†u(t, z) + Î¾(z)u(t, z) on (0,âˆž) Ã— Z with random potential (Î¾(z) : z âˆˆ Z). We consider independent andâ€¦ (More)

We study the parabolic Anderson problem, i.e., the heat equation âˆ‚tu = âˆ†u + Î¾u on (0,âˆž) Ã— Z d with independent identically distributed random potential {Î¾(z) : z âˆˆ Z} and localised initial conditionâ€¦ (More)

We consider a classical dilute particle system in a large box with pairinteraction given by a Lennard-Jones-type potential. The inverse temperature is picked proportionally to the logarithm of theâ€¦ (More)

We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than Îµ, agrees up to generation K with a regular Î¼-ary tree, where Î¼ is the essential minimum of theâ€¦ (More)

converges weakly to a probability measure Î¼0 supported by A. The measure Î¼0 is called the induced Minkowskior surface measure. In this paper, we investigate Minkowski-regularity and surface measuresâ€¦ (More)

We construct the surface measure on the space C([0, 1],M) of paths in a compact Riemannian manifold M without boundary embedded into Rn which is induced by the usual flat Wiener measure on C([0, 1],â€¦ (More)

We present a new approach to sound compression, based on rough path theory, which turns out to be more effective than the traditional Fourier and Wavelet methods. We describe a procedure for encodingâ€¦ (More)

The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus onâ€¦ (More)

It has recently been proved that a continuous path of bounded variation in Rd can be characterised in terms of its transform into a sequence of iterated integrals called the signature of the path.â€¦ (More)