Related papers: Crowding at the Front of the Marathon Packs
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the…
We study one-dimensional discrete as well as continuous time random walks, either with a fixed number of steps (for discrete time) $n$ or on a fixed time interval $T$ (for continuous time). In both cases, we focus on symmetric probability…
Finding a target in a complex environment is a fundamental challenge in nature, from chemical reactions to sperm reaching an egg. An effective strategy to reduce the time needed to reach a target is to deploy many searchers, increasing the…
In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…
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…
Scramble intersections stand as compelling examples of complex systems, shedding light on the pressing challenge of urban mobility. In this paper, we introduce a model aimed at unraveling the statistical intricacies of pedestrian crossing…
A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…
Paired comparison data considered in this paper originate from the comparison of a large number N of individuals in couples. The dataset is a collection of results of contests between two individuals when each of them has faced n opponents,…
Pedestrians are often encountered walking in the company of some social relations, rather than alone. The social groups thus formed, in variable proportions depending on the context, are not randomly organised but exhibit distinct features,…
Consider continuous-time random walks on Cayley graphs where the rate assigned to each edge depends only on the corresponding generator. We show that the limiting speed is monotone increasing in the rates for infinite Cayley graphs that…
We study statistics of the gaps in Random Average Process (RAP) on a ring with particles hopping symmetrically, except one tracer particle which could be driven. These particles hop either to the left or to the right by a random fraction…
We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…
Counting people in dense crowds is a demanding task even for humans. This is primarily due to the large variability in appearance of people. Often people are only seen as a bunch of blobs. Occlusions, pose variations and background clutter…
We consider random walks, say $W_n=(M_0, M_1,\dots, M_n)$, of length $n$ starting at 0 and based on the martingale sequence $M_k$ with differences $X_m=M_m-M_{m-1}$. Assuming that the differences are bounded, $|X_m|\leq 1$, we solve the…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
In high-density crowds, local motion can propagate, amplify, and lead to macroscopic phenomena, including 'density waves'. These density waves only occur when individuals interact, and impulses are transferred to neighbours. How this…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
In this paper a comparison between first order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number $N$ of pedestrians. The novelty is the fact of considering massive agents, namely…
We study the statistical distribution of the closest encounter between observations computed along different trajectories of a mixing dynamical system. At the limit of large trajectories, the distribution is of Gumbel type and depends on…
Among natural biological flocks/swarms or even mass social activities, when the collective behaviors of the followers has been dominated by the moving direction or opinion of one leader group, it seems very difficult for later-coming…