On multiple-particle continuous-time random walks

[摘要] Scaling limits of continuous-time random walks are used inphysics to model anomalous diffusion in which particles spread ata different rate than the classical Brownian motion. In thispaper, we characterize the scaling limit of the average ofmultiple particles, independently moving as a continuous-timerandom walk. The limit is taken by increasing the number ofparticles and scaling from microscopic to macroscopic view. Weshow that the limit is independent of the order of these limitingprocedures and can also be taken simultaneously in bothprocedures. Whereas the scaling limit of a single-particlemovement has quite an obscure behavior, the multiple-particleanalogue has much nicer properties.

[学科分类] 应用数学