Related papers: L\'evy walks on lattices as multi-state processes
We revisit the statistics of extremes and records of symmetric random walks with stochastic resetting, extending earlier studies in several directions. We put forward a diffusive scaling regime (symmetric step length distribution with…
We study a simple one dimensional sluggish random walk model with subdiffusive growth. In the continuum hydrodynamic limit, the model corresponds to a particle diffusing on a line with a space dependent diffusion constant D(x)=…
The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to…
We present an extensive analysis of transport properties in superdiffusive two dimensional quenched random media, obtained by packing disks with radii distributed according to a L\'evy law. We consider transport and scaling properties in…
A stochastic process with movement, return, and rest phases is considered in this paper. For the movement phase, the particles move following the dynamics of Gaussian process or ballistic type of L\'evy walk, and the time of each movement…
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which…
The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit…
We consider the dynamics of a separable Continuous Time Random Walk (CTRW) when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid…
In this work we introduce discrete-time quantum walks in state space, more precisely on Fock-state lattices. Fock-state lattices provide a natural and clean setting for implementing lattice models, particularly in quantum optical systems.…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Gr\"unbaum--Moral--Vel\'azquez, this enables us to study spreading rates for quantum walks in one…
Investigating the behavior of noninteracting fermions subjected to local dephasing, we reveal that quasi-particle dephasing can induce superdiffusive transport. This superdiffusion arises from nodal points within the momentum distribution…
In this paper, we study a stochastically driven non-equilibrium quantum system where the driving protocols consist of hopping and waiting processes. The waiting times between two hopping processes satisfy a heavy-tailed distribution. By…
We consider a random walk on one-dimensional inhomogeneous graphs built from Cantor fractals. Our study is motivated by recent experiments that demonstrated superdiffusion of light in complex disordered materials, thereby termed L\'evy…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
We investigate the quantum walk and the quantum kicked rotor in resonance subjected to noise with a L\'evy waiting time distribution. We find that both systems have a sub-ballistic wave function spreading as shown by a power-law tail of the…
The propagation of light that undergoes multiple-scattering by resonant atomic vapor can be described as a L\'evy flight. L\'evy flight is a random walk with heavy tailed step-size (r) distribution, decaying asymptotically as $P(r)\sim…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…
We study the relation between flow structure and fluid deformation in steady two-dimensional random flows. Beyond the linear (shear flow) and exponential (chaotic flow) elongation paradigms, we find a broad spectrum of stretching behaviors,…
This paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process…