A huge variety of natural phenomena, including prey-predator interaction, chemical reaction kinetics, foraging, and pharmacokinetics, are mathematically described as encounters between entities performing a random motion on an appropriate structure. On homogeneous structures, two random walkers meet with certainty if and only if the structure is recurrent, i.e., a single random walker returns to its starting point with probability 1. We prove here that this property does not hold on general inhomogeneous structures, and introduce the concept of two-particle transience, providing examples of realistic recurrent structures where two particles may never meet if they both move, while an encounter is certain if either stays put. We anticipate that our results will pave the way for the study of the effects of geometry in a wide array of natural phenomena involving interaction between randomly moving agents.

Random collisions on branched networks: How simultaneous diffusion prevents encounters in inhomogeneous structures / R., Campari; Cassi, Davide. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 86:(2012), pp. 021110-021113. [10.1103/PhysRevE.86.021110]

Random collisions on branched networks: How simultaneous diffusion prevents encounters in inhomogeneous structures

CASSI, Davide
2012-01-01

Abstract

A huge variety of natural phenomena, including prey-predator interaction, chemical reaction kinetics, foraging, and pharmacokinetics, are mathematically described as encounters between entities performing a random motion on an appropriate structure. On homogeneous structures, two random walkers meet with certainty if and only if the structure is recurrent, i.e., a single random walker returns to its starting point with probability 1. We prove here that this property does not hold on general inhomogeneous structures, and introduce the concept of two-particle transience, providing examples of realistic recurrent structures where two particles may never meet if they both move, while an encounter is certain if either stays put. We anticipate that our results will pave the way for the study of the effects of geometry in a wide array of natural phenomena involving interaction between randomly moving agents.
2012
Random collisions on branched networks: How simultaneous diffusion prevents encounters in inhomogeneous structures / R., Campari; Cassi, Davide. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 86:(2012), pp. 021110-021113. [10.1103/PhysRevE.86.021110]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2513893
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