2024/02/12 by Manuel González-Navarrete, González-Navarrete, Manuel, Rodrigo Lambert +3
Mathematics · #FOS: Mathematics #G.3 #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2402.08033
openalex publication_date 2024/02/12 · openalex created_date 2024/02/15 · openalex updated_date 2026/07/28
Based on a martingale theory approach, we present a complete characterization of the asymptotic behaviour of a lazy reinforced random walk (LRRW) which shows three different regimes (diffusive, critical and superdiffusive). This allows us to prove versions of the law of large numbers, the quadratic strong law, the law of iterated logarithm, the almost sure central limit theorem and the functional central limit theorem in the diffusive and critical regimes. In the superdiffusive regime we obtain a strong convergence to a random variable, including a central limit theorem and a law of iterated logarithm for the fluctuations.