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Related papers: Large Deviation in Continuous Time Random Walks

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The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw_1), a random walk along the line of natural time, happening in operational time; (rw_2), a…

Probability · Mathematics 2011-04-21 Rudolf Gorenflo , Francesco Mainardi

We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and…

Disordered Systems and Neural Networks · Physics 2015-06-12 R. Burioni , G. Gradenigo , A. Sarracino , A. Vezzani , A. Vulpiani

Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the…

Statistical Mechanics · Physics 2022-03-23 Wanli Wang , Eli Barkai , Stanislav Burov

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…

Statistical Mechanics · Physics 2015-06-24 R. Hilfer

We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are…

Statistical Mechanics · Physics 2020-07-01 Anna S. Bodrova , Igor M. Sokolov

Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take…

Statistical Mechanics · Physics 2018-09-13 Trifce Sandev , Weihua Deng , Pengbo Xu

Many stochastic time series can be modelled by discrete random walks in which a step of random sign but constant length $\delta x$ is performed after each time interval $\delta t$. In correlated discrete time random walks (CDTRWs), the…

Quantitative Methods · Quantitative Biology 2012-07-06 Claus Metzner

We study large deviations for random walks on stratified (Carnot) Lie groups. For such groups, there is a natural collection of vectors which generates their Lie algebra, and we consider random walks with increments in only these…

Probability · Mathematics 2024-08-16 Maria Gordina , Tai Melcher , Dan Mikulincer , Jing Wang

We consider the branching random walk drifting to $-\infty$ and we investigate large deviations-type estimates for the first passage time. We prove the corresponding law of large numbers and the central limit theorem.

Probability · Mathematics 2017-09-14 Dariusz Buraczewski , Mariusz Maslanka

Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their…

Probability · Mathematics 2014-07-25 Mark M. Meerschaert , Peter Straka

We consider a random walk in a random environment (RWRE) on the strip of finite width $\mathbb{Z} \times \{1,2,\ldots,d\}$. We prove both quenched and averaged large deviation principles for the position and the hitting times of the RWRE.…

Probability · Mathematics 2016-06-20 Jonathon Peterson

We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…

Statistical Mechanics · Physics 2011-05-02 S. I. Denisov , H. Kantz

Consider a random walk in random environment on a supercritical Galton--Watson tree, and let $\tau_n$ be the hitting time of generation $n$. The paper presents a large deviation principle for $\tau_n/n$, both in quenched and annealed cases.…

Probability · Mathematics 2011-01-11 Elie Aidekon

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…

Statistical Mechanics · Physics 2021-10-25 Gaia Pozzoli , Mattia Radice , Manuele Onofri , Roberto Artuso

We study the dynamics of a radioactive species flowing through a porous material, within the Continuous-Time Random Walk (CTRW) approach to the modelling of stochastic transport processes. Emphasis is given to the case where radioactive…

Statistical Mechanics · Physics 2008-05-17 A. Zoia

We study numerically the distributions of the length $L$ of the longest increasing subsequence (LIS) for the two cases of random permutations and of one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able…

Disordered Systems and Neural Networks · Physics 2019-04-05 Jörn Börjes , Hendrik Schawe , Alexander K. Hartmann

We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…

Statistical Mechanics · Physics 2015-06-23 R. Burioni , G. Gradenigo , A. Sarracino , A. Vezzani , A. Vulpiani

Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…

Statistical Mechanics · Physics 2010-11-24 S. I. Denisov , H. Kantz

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…

Statistical Mechanics · Physics 2023-07-28 Alexander K. Hartmann , Alexandre Krajenbrink , Pierre Le Doussal

The Semi-Markov property of Continuous Time Random Walks (CTRWs) and their limit processes is utilized, and the probability distributions of the bivariate Markov process $(X(t),V(t))$ are calculated: $X(t)$ is a CTRW limit and $V(t)$ a…

Statistical Mechanics · Physics 2016-07-20 G. Gill , P. Straka