Related papers: Local time for run and tumble particle
In this paper, we study a transient spatially inhomogeneous random walk with asymptotically zero drifts on the lattice of the positive half line. We give criteria for the finiteness of the number of points having exactly the same local time…
The way particles interact with turbulent structures, particularly in regions of high vorticity and strain rate, has been investigated in simulations of homogeneous turbulence and in simple flows which have a periodic or persistent…
We study local power fluctuations in numerical simulations of stationary, homogeneous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the…
We study the support (i.e. the set of visited sites) of a t step random walk on a two-dimensional square lattice in the large t limit. A broad class of global properties M(t) of the support is considered, including, e.g., the number S(t) of…
In this paper, we first prove that the local time associated with symmetric $\alpha$-stable processes is of bounded $p$-variation for any $p>\frac{2}{\alpha-1}$ partly based on Barlow's estimation of the modulus of the local time of such…
We analyzed formation of small-scale inhomogeneities of particle spatial distribution (particle clustering) in a turbulent flow. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution,…
Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is…
We consider an active run-and-tumble particle (RTP) in $d$ dimensions, starting from the origin and evolving over a time interval $[0,t]$. We examine three different models for the dynamics of the RTP: the standard RTP model with…
Diffusion with stochastic resetting has recently emerged as a powerful modeling tool with a myriad of potential applications. Here, we study local time in this model, covering situations of free and biased diffusion with, and without, the…
The time dependence of the survival probability, S(t), is determined for diffusing particles in two dimensions which are also driven by a random unidirectional zero-mean velocity field, v_x(y). For a semi-infinite system with unbounded y…
We investigate the interplay between nonlinearity and inhomogeneities in discrete-time quantum walks on one-dimensional lattices. Nonlinear effects are introduced through a Kerr-like, intensity-dependent local phase, while spatial and…
We investigate steady-state current fluctuations in two models of run-and-tumble particles (RTPs) on a ring of $L$ sites, for \textit{arbitrary} tumbling rate $\gamma=\tau_p^{-1}$ and density $\rho$; model I consists of standard hardcore…
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
We study the long-time behavior of the probability density Q_t of the first exit time from a bounded interval [-L,L] for a stochastic non-Markovian process h(t) describing fluctuations at a given point of a two-dimensional, infinite in both…
Let \alpha ([0,1]^p) denote the intersection local time of p independent d-dimensional Brownian motions running up to the time 1. Under the conditions p(d-2)<d and d\ge 2, we prove lim_{t\to\infty}t^{-1}\log P\bigl{\alpha([0,1]^p)\ge…
The dynamics of a subdiffusive continuous time random walker in an inhomogeneous environment is analyzed. In each microscopic jump, a random time is drawn from a waiting time probability density function (WT-PDF) that decays as a power law:…
We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are…
We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…
We study the positive occupation time of a run-and-tumble particle (RTP) subject to stochastic resetting. Under the resetting protocol, the position of the particle is reset to the origin at a random sequence of times that is generated by a…
The visit probability, quantifying whether a particle has reached a given point for the first time by a specified time, provides access to various extreme value statistics and serves as a fundamental tool for characterising active matter…