Biomedical subjects

Alain Comtet

Publications and source records attributed to Alain Comtet.

4 recordsLinked to original sources

PubMed2006

Statistical properties of functionals of the paths of a particle diffusing in a one-dimensional random potential.

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism in two specific examples: (1) where the functional corresponds to the local time spent by the particle around the origin and (2) where the functional corresponds to the occupation time spent by the particle on the positive side of the origin, within an observation time window of size t. We compute the disorder average distributions of the local time, the inverse local time, the occupation time, and the inverse occupation time and show that in many cases disorder modifies the behavior drastically.

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PubMed2004

Exact maximal height distribution of fluctuating interfaces.

We present an exact solution for the distribution P(h(m),L) of the maximal height h(m) (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h(m),L)=L(-1/2)f(h(m)L(-1/2)) for all L>0, where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds, but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.

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PubMed2002

Exact asymptotic results for persistence in the Sinai model with arbitrary drift.

We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a method that maps the problem of computing the persistence to the problem of finding the energy spectrum of a single-particle quantum Hamiltonian, which can be subsequently found. Our method allows us analytical access to arbitrary values of the drift (bias), thus going beyond the previous methods that provide results only in the limit of vanishing drift. We show that on varying the drift the persistence displays a variety of rich asymptotic behaviors including, in particular, interesting qualitative changes at some special values of the drift.

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PubMed2002

Local and occupation time of a particle diffusing in a random medium.

We consider a particle moving in a one-dimensional potential which has a symmetric deterministic part and a quenched random part. We study analytically the probability distributions of the local time (spent by the particle around its mean value) and the occupation time (spent above its mean value) within an observation time window of size t. In the absence of quenched randomness, these distributions have three typical asymptotic behaviors depending on whether the deterministic potential is unstable, stable, or flat. These asymptotic behaviors are shown to get drastically modified when the random part of the potential is switched on, leading to the loss of self-averaging and wide sample to sample fluctuations.

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