2017/11/14 by Vincent Beffara, Beffara, Vincent, Cong Bang Huynh +1
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1711.05527
openalex publication_date 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when the bias converges to its critical value is conjectured to coincide with the weak limit of the uniform SAW. Along the way, we obtain a criterion for the continuity of the escape probability of a biased random walk on a tree as a function of the bias, and show that the collection of escape probability functions for spherically symmetric trees of bounded degree is stable under uniform convergence.