Related papers: L\'{e}vy flights in random environments

We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. The three different bicritical static…

We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous nonequilibrium phase transition from a condensed phase, in which a single `flock'…

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

Quenched disorder - in the sense of the Harris criterion - is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we…

We study the statistics of increments in record values in a time series $\{x_0=0,x_1, x_2, \ldots, x_n\}$ generated by the positions of a random walk (discrete time, continuous space) of duration $n$ steps. For arbitrary jump length…

We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from 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…

We study the scaling properties of critical particle systems confined by a potential. Using renormalization-group arguments, we show that their critical behavior can be cast in the form of a trap-size scaling, resembling finite-size scaling…

We explore the dynamics of long-range Kitaev chain by varying pairing interaction exponent, $\alpha$. It is well known that distinctive characteristics on the nonequilibrium dynamics of a closed quantum system are closely related to the…

We study the two-dimensional contact process (CP) with quenched disorder (DCP), and determine the static critical exponents beta and nu_perp. The dynamic behavior is incompatible with scaling, as applied to models (such as the pure CP) that…

We address L\'{e}vy-stable stochastic processes in bounded domains, with a focus on a discrimination between inequivalent proposals for what a boundary data-respecting fractional Laplacian (and thence the induced random process) should…

Spatial L{\'{e}}vy-like flights are introduced as a way in the absorbing phase transitions to produce non-local interactions. We utilize the autoencoder, an unsupervised learning method, to predict the critical points for $(1+1)$-d directed…

This paper investigates stability analysis of flapping flight. Due to time-varying aerodynamic forces, such systems do not display fixed points of equilibrium. The problem is therefore approached via a limit cycle analysis based on Floquet…

The non-equilibrium random-field Ising model is well studied, yet there are outstanding questions. In two dimensions, power law scaling approaches fail and the critical disorder is difficult to pin down. Additionally, the presence of…

The L\'evy walk process for a lower interval of an excursion times distribution ($\alpha<1$) is discussed. The particle rests between the jumps and the waiting time is position-dependent. Two cases are considered: a rising and diminishing…

We consider the continuous-time random walk of a particle in a two-dimensional self-affine quenched random potential of Hurst exponent $H>0$. The corresponding master equation is studied via the strong disorder renormalization procedure…

We explore the nonunitary dynamics of $(2+1)$-dimensional free fermions and show that the obtained steady state is critical regardless the strength of the nonunitary evolution. Numerical results indicate that the entanglement entropy has a…

We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at $x_0\geq0$, where successive jumps are drawn independently…

Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted L\'evy processes. The latter is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable…

We employed the method of virial expansion in order to compute the retarded density correlation function (generalized diffusion propagator) in the critical random matrix ensemble in the limit of strong multifractality. We found that the…