Related papers: Continuous time random walk for open systems: Fluc…
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…
For thermostatted dissipative systems the Fluctuation Theorem gives an analytical expression for the ratio of probabilities that the time averaged entropy production in a finite system observed for a finite time, takes on a specified value…
This is the third in a series of papers in which we consider one-dimensional Random Walk in Cooling Random Environment (RWCRE). The latter is obtained by starting from one-dimensional Random Walk in Random Environment (RWRE) and resampling…
The thermodynamic uncertainty relation (TUR) provides a universal entropic bound for the precision of the fluctuation of the charge transfer for example for a class of continuous time stochastic processes. However, its extension to general…
We study the statistics of the first passage of a random walker to absorbing subsets of the boundary of compact domains in different spatial dimensions. We describe a novel diagnostic method to quantify the trajectory-to-trajectory…
We consider the limit behavior of an excited random walk (ERW), i.e., a random walk whose transition probabilities depend on the number of times the walk has visited to the current state. We prove that an ERW being naturally scaled…
We study analytically, in one dimension, the survival probability $P_{s}(t)$ up to time $t$ of an immobile target surrounded by mutually noninteracting traps each performing a continuous-time random walk (CTRW) in continuous space. We…
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…
We consider a recent model of random walk that recursively grows the network on which it evolves, namely the Tree Builder Random Walk (TBRW). We introduce a bias $\rho \in (0,\infty)$ towards the root, and exhibit a phase transition for…
We consider a discrete-time random walk on a one-dimensional lattice with space and time-dependent random jump probabilities, known as the Beta random walk. We are interested in the probability that, for a given realization of the jump…
We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…
We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two…
An investigation of the distribution of finite time trajectory divergence is performed on an Atmospheric Global Circulation Model. The distribution of the largest local Lyapunov exponent shows a significant probability for negative values…
In high-frequency financial data not only returns, but also waiting times between consecutive trades are random variables. Therefore, it is possible to apply continuous-time random walks (CTRWs) as phenomenological models of the…
Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many…
The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into…
We consider the single-file dynamics of $N$ identical random walkers moving with diffusivity $D$ in one dimension (walkers bounce off each other when attempting to overtake). Additionally, we require that the separation between neighboring…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
The dissipation function for a system is defined as the natural logarithm of the ratio between probabilities of a trajectory and its time-reversed trajectory, and its probability distribution follows a well-known relation called the…
Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT)…