PreprintCC BY 4.0arXiv
Random walk in a null recurrent birth-and-death dynamical environment
Abstract
We study a random walk in ℤd in a dynamical random environment constituted of independent null recurrent birth-and-death chains, and establish a scaling limit result for the position of the walker in terms of a sublinear time change of Brownian motion, thus establishing subdiffusivity, in contrast to a diffusivity result established previously in an ergodic version of the model.
Related
- Circular Rearrangement Inequality and Optimal Cyclic Birth and Death Chains
- Cumulative Rewards for Birth–Death Processes with Catastrophes
- Darboux transformations of linear birth-death processes
- Space-time large deviations for continuum birth-and-death processes
- Invasion dynamics with vanishing fitness for a quasi-critical birth-death process
BibTeX
@misc{fontes2026random,
title = {{Random walk in a null recurrent birth-and-death dynamical environment}},
author = {Luiz Renato Fontes and Pablo A. Gomes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08383},
eprint = {2610.08383},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08383},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Random walk in a null recurrent birth-and-death dynamical environment
AU - Luiz Renato Fontes
AU - Pablo A. Gomes
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08383
UR - https://arxiv.org/abs/2610.08383
AB - We study a random walk in ℤ^d in a dynamical random environment constituted of independent null recurrent birth-and-death chains, and establish a scaling limit result for the position of the walker in terms of a sublinear time change of Brownian motion, thus establishing subdiffusivity, in contrast to a diffusivity result established previously in an ergodic version of the model.
ER -