Related papers: On interactive anisotropic walks in two dimensions…
Analytical approaches in models of opinion formation have been extensively studied either for an opinion represented as a discrete or a continuous variable. In this paper, we analyze a model which combines both approaches. The state of an…
Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d. in space, and its…
We study L\'evy walks in quenched disordered one-dimensional media, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling relations for the random-walk probability and for the resistivity in the equivalent…
We study a generalized Hadamard walk in one dimension with three inner states. The particle governed by the three-state quantum walk moves, in superposition, both to the left and to the right according to the inner state. In addition to…
A one-dimensional confined Nonlinear Random Walk is a tuple of $N$ diffeomorphisms of the unit interval driven by a probabilistic Markov chain. For generic such walks, we obtain a geometric characterization of their ergodic stationary…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
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…
Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…
We review some recent results obtained in the framework of the 2-dimensional Interacting Self-Avoiding Walk (ISAW). After a brief presentation of the rigorous results that have been obtained so far for ISAW we focus on the Interacting…
In a system made up of independent random walks, fluctuations of order $n^{1/4}$ from the hydrodynamic limit come from particle current across characteristics. We show that a two-parameter space-time particle current process converges to a…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
This paper introduces a class of non-linear and continuous-time opinion dynamics model with additive noise and state dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power…
Quantum walk is a synonym for multi-path interference and faster spread of a particle in a superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational…
Quantum random walks are constructed on operator spaces with the aid of matrix-space lifting, a type of ampliation intermediate between those provided by spatial and ultraweak tensor products. Using a form of Wiener-Ito decomposition, a…
A bouncing drop and its associated accompanying wave forms a walker. Based on previous works, we show in this article that it is possible to formulate a simple theoretical framework for the walker dynamics. It relies on a time scale…
Most mathematical models of opinion dynamics treat attitudes as scalar quantities or positions on a low-dimensional ideological axis. Empirical attitudes, however, are bundles of positions across many policy issues, and the geometry of the…
We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are…
In this work we study the opinion evolution in a community-based population with intergroup interactions. We address two issues. First, we consider that such intergroup interactions can be negative with some probability $p$. We develop a…
We explore the distribution of paths followed in fluctuation-induced switching between coexisting stable states. We introduce a quantitative characteristic of the path distribution in phase space that does not require a priori knowledge of…