{"paper":{"title":"Limit theorems for random walks with spatio-temporal drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Random walks with position-and-time dependent polynomial drift show three distinct asymptotic regimes.","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ngo P.N. Ngoc, Tuan-Minh Nguyen","submitted_at":"2026-05-18T01:06:11Z","abstract_excerpt":"We study a class of discrete-time random walks in $\\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models of self-interacting random processes. We determine the asymptotic behavior of the walk under the assumption that its increments have moments of order $p$ for some $p>2$. In the linear case, where the drift depends linearly on the current position, we establish a phase transition in the convergence in distribution of the normalized process to Gaussian limits. 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