An invariance principle and a large deviation principle for the biased random walk on ${\mathbb{Z}}^{\lowercase{\textbf{\textit{d}}}}$. (March 2020)

• Record Type: Journal Article
• Authors: Liu, Yuelin; Sidoravicius, Vladas; Wang, Longmin; Xiang, Kainan
• Is Part Of: Journal of applied probability. Volume 57:Number 1(2020)
• Page Start: 295
• Page End: 313
• Publication Date: 2020-03
• Subjects: Biased random walk, -- invariance principle, -- large deviation principle; 60J10, -- 05C81, -- 60F05, -- 60F10; 519.2
• DOI: 10.1017/jpr.2019.92
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: We establish an invariance principle and a large deviation principle for a biased random walk ${\text{RW}}_\lambda$ with $\lambda\in [0, 1)$ on $\mathbb{Z}^d$ . The scaling limit in the invariance principle is not a d -dimensional Brownian motion. For the large deviation principle, its rate function is different from that of a drifted random walk, as may be expected, though the reflected biased random walk evolves like the drifted random walk in the interior of the first quadrant and almost surely visits coordinate planes finitely many times.