Random Walks on Finite Discrete Velocity Fields
DOI:
https://doi.org/10.5540/03.2026.012.01.0330Palavras-chave:
Discrete Velocity Fields, Lagrangian Processes, Markov Chains, EigenvaluesResumo
This work presents a discrete-time random velocity field on a class of one-dimensional finite lattices with periodic boundary conditions. We define the Eulerian and Lagrangian location processes, analyzing their relationship through circulant and permutation transition matrices. By examining the second-largest eigenvalue modulus, we characterize the convergence rate of the Lagrangian location process to its invariant distribution. We explore how spatial domain size and parity influence convergence behavior, providing insights into stochastic transport dynamics in discrete settings.
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Referências
C. D. Bennett and C. L. Zirbel. “Discrete velocity fields with explicitly computable Lagrangian law”. In: Journal of Statistical Physics 111 (2003), pp. 681–701.
S. Corrsin. “Atmospheric diffusion and air pollution”. In: Advances in Geophysics 6 (1959), p. 161.
F. W. Elliott and A. J. Majda. “Pair dispersion over an inertial range spanning many decades”. In: Physics of Fluids 8.4 (1996), pp. 1052–1060.
S. T. Garren and R. L. Smith. “Estimating the second largest eigenvalue of a Markov transition matrix”. In: Bernoulli 6.2 (2000), pp. 215–242.
D. A. Levin and Y. Peres. Markov chains and mixing times. Vol. 107. American Mathematical Soc., 2017.
G. I. Taylor. “Statistical Theory of Turbulence”. In: Proceedings of the Royal Society of London A 151.873 (1935), pp. 421–444.
W. A. Woyczynski. “Passive tracer transport in stochastic flows”. In: Stochastic Climate Models 49 (2012), pp. 385–396.
C. L. Zirbel. “Lagrangian observations of homogeneous random environments”. In: Advances in Applied Probability (2001), pp. 810–835.
