相关论文: Record Ages of Scale Invariant non-Markovian Rando…

The record age tau_k, defined as the time between the k-th and k+1-st record-breaking events, is a central observable of extreme-value statistics. In Markovian processes, the absence of memory makes tau_k independent of k. How memory breaks…

The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the…

We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a L\'evy flight on a line. After a brief survey of the theory of records for independent and…

The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise…

We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the integral of Brownian motion. In this…

In recent years there has been a surge of interest in the statistics of record-breaking events in stochastic processes. Along with that, many new and interesting applications of the theory of records were discovered and explored. The record…

The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…

We study the record statistics of random walks after $n$ steps, $x_0, x_1,\ldots, x_n$, with arbitrary symmetric and continuous distribution $p(\eta)$ of the jumps $\eta_i = x_i - x_{i-1}$. We consider the age of the records, i.e. the time…

This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influences future dynamics, we uncover new mechanisms and…

We develop a comprehensive framework for analyzing full record statistics, covering record counts $M(t_1), M(t_2), \ldots$, and their corresponding attainment times $T_{M(t_1)}, T_{M(t_2)}, \ldots$, as well as the intervals until the next…

Record statistics is the study of how new highs or lows are created and sustained in any dynamical process. The study of the highest or lowest records constitute the study of extreme values. This paper represents an exploration of record…

In this paper we consider the age-related alterations of heart rate variability on the basis of the study of non-Markovian effects. The age dynamics of relaxation processes is quantitatively described by means of local relaxation…

In recent years it has become clear that the brain maintains a temporal memory of recent events stretching far into the past. This paper presents a neurally-inspired algorithm to use a scale-invariant temporal representation of the past to…

In classical physics, memoryless dynamics and Markovian statistics are one and the same. This is not true for quantum dynamics, first and foremost because quantum measurements are invasive. Going beyond measurement invasiveness, here we…

1. Animal movement patterns contribute to our understanding of variation in breeding success and survival of individuals, and the implications for population dynamics. 2. Over time, sensor technology for measuring movement patterns has…

The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…

The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…

Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale…

It is shown that statistics of records for time series generated by random walks are independent of the details of the jump distribution, as long as the latter is continuous and symmetric. In N steps, the mean of the record distribution…

The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that…