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The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…

Statistical Finance · Quantitative Finance 2015-05-28 Mauro Politi , Nicolas Millot , Anirban Chakraborti

The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate…

Soft Condensed Matter · Physics 2015-06-16 Rodrigo Soto , Ramin Golestanian

We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…

Condensed Matter · Physics 2007-05-23 Irene Giardina , Jean-Philippe Bouchaud , Marc Mezard

We propose a macroscopic model in form of a dispersion-transport equation for non-congested flow of the athletes which is coupled to a kinematic-wave model for congested flow. The model takes into account the performance (i.e., free-flow…

Physics and Society · Physics 2014-12-19 Martin Treiber

In this paper, we present results of an entrance experiment investigating the effect of the corridor width in front of a bottleneck on the density. The idea is based on a previous study suggesting that a guiding system in front of an…

Physics and Society · Physics 2020-07-14 Juliane Adrian , Maik Boltes , Stefan Holl , Anna Sieben , Armin Seyfried

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of…

Physics and Society · Physics 2018-09-06 A. Ciallella , E. N. M. Cirillo , P. L. Curseu , A. Muntean

Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…

Physics and Society · Physics 2021-08-11 Daniel B. Wilson , Francis G. Woodhouse , Matthew J. Simpson , Ruth E. Baker

We study the spacing of the primes using methods from information theory. In information theory, the equivalence of continuous and discrete representations of information is established by Shannon sampling theory. Here, we use Shannon…

Number Theory · Mathematics 2018-08-03 Nicholas Pun , Robert T. W. Martin , Achim Kempf

Extreme events such as earthquakes, floods, and power blackouts often display burst phenomena where multiple extreme events occur in quick succession or in bunches. This study examines bunching of extreme events on a complex network using a…

Physics and Society · Physics 2025-09-24 Sarvesh K. Upadhyay , Vimal Kishore , Sanjay Kumar , R. E. Amritkar

We identify a fundamental phenomenon of heterogeneous one dimensional random walks: the escape (traversal) time is maximized when the heterogeneity in transition probabilities forms a pyramid-like potential barrier. This barrier corresponds…

Probability · Mathematics 2020-07-29 Asaf Cassel , Shie Mannor , Guy Tennenholtz

We introduce a model of interacting random walkers on a finite one dimensional chain with absorbing boundaries or targets at the ends. Walkers are of two types: informed particles that move ballistically towards a given target, and…

Statistical Mechanics · Physics 2015-02-20 Ricardo Martinez-Garcia , Cristobal Lopez , Federico Vazquez

We introduce a toy model of the "rat race" in which individuals try to better themselves relative to the rest of the population. An individual is characterized by a real-valued fitness and each advances at a constant rate by an amount that…

Physics and Society · Physics 2007-05-23 D. ben-Avraham , Satya N. Majumdar , S. Redner

A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…

Machine Learning · Computer Science 2018-01-08 Reinhard Heckel , Max Simchowitz , Kannan Ramchandran , Martin J. Wainwright

We develop a model to compute the first-passage time of a random walker in a crowded environment. Hard-core particles with the same size and diffusion coefficient than the tracer diffuse, and the model allows to compute the first passage…

Statistical Mechanics · Physics 2017-02-27 Vincent Tejedor

The athletic achievements of African athletes in global running championships have long been subject to scientific and sociological inquiry. During the 1990s, a popular narrative emerged, suggesting that West African lineage conferred…

Physics and Society · Physics 2024-03-06 Tade Souaiaia , Nabie Fofanah , Rawle DeLisle , Sheena Mason

The statistical modelling of spatial extremes has recently made major advances. Much of its focus so far has been on the modelling of the magnitudes of extreme events but little attention has been paid on the timing of extremes. To address…

Statistics Theory · Mathematics 2015-03-20 Clément Dombry , Mathieu Ribatet , Stilian Stoev

Competition for a limited resource is the hallmark of many complex systems, and often, that resource turns out to be the physical space itself. In this work, we study a novel model designed to elucidate the dynamics and emergence in complex…

Physics and Society · Physics 2026-03-18 Ann Mary Mathew , V Sasidevan

Professional sports enhance interaction among athletes through training groups, sponsored events and competitions. Among these, the Olympic Games represent the largest competition with a global impact, providing the participants with a…

Physics and Society · Physics 2024-10-29 Jorge P. Rodríguez , Lluís Arola-Fernández

We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…

Probability · Mathematics 2011-12-07 Ofer Zeitouni , Ming Fang

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the…

Statistical Mechanics · Physics 2012-05-31 Vimal Kishore , M. S. Santhanam , R. E. Amritkar