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Continuous time random walks and the Cauchy problem for the heat equation
(Springer, 2018-10)
We deal with anomalous diffusions induced by continuous time random walks - CTRW in ℝn. A particle moves in ℝn in such a way that the probability density function u(·, t) of finding it in region Ω of ℝn is given by ∫Ωu(x, ...
Exceptional times for the dynamical discrete web
(ELSEVIER SCIENCE BV, 2009)
The dynamical discrete web (DyDW), introduced in the recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter ...
Fluctuations of the front in a stochastic combustion model
(GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2007)
We consider an interacting particle system on the one-dimensional lattice Z modeling combustion. The process depends on two integer parameters 2 <= a <= M <= infinity. Particles move independently as continuous time simple ...
Reaction rate in an evanescent random walkers system
(2015)
Diffusion mediated reaction models are particularly ubiquitous in the description of phys-ical, chemical or biological processes. The random walk schema is a useful tool for formu-lating these models. Recently, evanescent ...
Random walks in static and markovian time-dependent random environment
(2014)
Firstly, we introduce ellipticity criteria for random walks in i.i.d. random environments,
under which we can extend the ballisticity conditions of Sznitman’s and the polynomial
effective criteria of Berger, Drewitz and ...
Asymptotic behavior of a stochastic combustion growth process
(EUROPEAN MATHEMATICAL SOC, 2004)
We study a continuous time growth process on the d-dimensional hypercubic lattice Z(d), which admits a phenomenological interpretation as the combustion reaction A + B --> 2A, where A represents heat particles and B inert ...
Ergodic transitions in continuous-time random walks
(Amer Physical SocCollege PkEUA, 2010)
Non-equilibrium transition from dissipative quantum walk to classical random walk
(IOP Publishing, 2012-07)
We have investigated the time evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence ...