Related papers: Elephant random walk with attributed steps and ext…

Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually…

We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively $\alpha$-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov…

We introduce a generalisation of Sch\"{u}tz and Trimper's elephant random walk to finitely generated groups. We focus on the simplest non-abelian setting, i.e. groups whose Cayley graphs are homogeneous trees of degree $d \ge 3$. We show…

We consider the Markovian supermarket model with growing choices, where jobs arrive at rate $n\lambda_n$ and each of $n$ parallel servers processes jobs in its queue at rate $1$. Each incoming job joins the shortest among $d_n \in…

We consider pricing in settings where a consumer discovers his value for a good only as he uses it, and the value evolves with each use. We explore simple and natural pricing strategies for a seller in this setting, under the assumption…

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as…

We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…

We consider two models of one-dimensional random walks among biased i.i.d. random conductances: the first is the classical exponential tilt of the conductances, while the second comes from the effect of adding an external field to a random…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial…

A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…

In this article we refine well-known results concerning the fluctuations of one-dimensional random walks. More precisely, if $(S_n)_{n \geq 0}$ is a random walk starting from 0 and $r\geq 0$, we obtain the precise asymptotic behavior as…

Two main procedures characterize the way in which social actors evaluate the qualities of the options in decision-making processes: they either seek to evaluate their intrinsic qualities (individual learners), or they rely on the opinion of…

We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…

Given the combined evidences of bounded rationality, limited information and short-term optimization, over-the-counter (OTC) fresh product markets provide a perfect instance where to develop a behavioural approach to the analysis of…

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…

To choose between two discrete goods, a consumer pays attention to only those with prices below a threshold. From these, she chooses her most preferred good. We assume consumers in a population have the same preference but may have…

The career of an employee can be described (under certain circumstances) by a random walk, where the states of the random walk are determined by the level and position of an employee. At each decision moment the state of the employee is…

We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…