相关论文: Exact statistics of record increments of random wa…

We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global…

We perform a thorough analysis of the survival probability of symmetric random walks with stochastic resetting, defined as the probability for the walker not to cross the origin up to time $n$. For continuous symmetric distributions of step…

We consider a model of space-continuous one-dimensional random walk with simple correlation between the steps: the probability that two consecutive steps have same sign is $q$ with $0\leq q\leq 1$. The parameter $q$ allows thus to control…

The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…

L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…

The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…

Building upon the knowledge of the distribution of the first positive position reached by a random walker starting from the origin, one can derive new results on the statistics of the gap between the largest and second-largest positions of…

We consider a random walk of $n$ steps starting at $x_0=0$ with a double exponential (Laplace) jump distribution. We compute exactly the distribution $p_{k,n}(\Delta)$ of the gap $d_{k,n}$ between the $k^{\rm th}$ and $(k+1)^{\rm th}$…

We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim |\eta|^p \,e^{-|\eta|}$, parametrized by a non-negative integer $p$. Our main focus is on…

We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width $p$ of a sequence of independent, identically distributed random variables. An asymptotic analysis of the general…

We consider one-dimensional discrete-time random walks (RWs) with arbitrary symmetric and continuous jump distributions $f(\eta)$, including the case of L\'evy flights. We study the expected maximum ${\mathbb E}[M_n]$ of bridge RWs, i.e.,…

The random walk process in a nonhomogeneous medium, characterised by a L\'evy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is…

We investigate the statistics of three kinds of records associated with planar random walks, namely diagonal, simultaneous and radial records. The mean numbers of these records grow as universal power laws of time, with respective exponents…

We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum…

In this paper, we deal with the asymptotic distribution of the maximum increment of a random walk with a regularly varying jump size distribution. This problem is motivated by a long-standing problem on change point detection for epidemic…

We provide a uniform framework to compute the exact distribution of the number of minima/maxima in three different random walk landscape models in one dimension. The landscape is generated by the trajectory of a discrete-time continuous…

Continuous time random walk models with decoupled waiting time density are studied. When the spatial one jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized…

In this paper, we study the large $n$ asymptotics of the expected maximum of an $n$-step random walk/L\'evy flight (characterized by a L\'evy index $1<\mu\leq 2$) on a line, in the presence of a constant drift $c$. For $0<\mu\leq 1$, the…

We investigate records in a growing sequence of identical and independently distributed random variables. The record equals the largest value in the sequence, and our focus is on the increment, defined as the difference between two…

We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$-distribution with parameter in the range $1/2 \leq \nu \leq 5$.…