2020/04/27 by Stefano Bonaccorsi, Bonaccorsi, Stefano, Francesca Cottini +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #advanced mathematical theories #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2004.12971
We study diffusion-type equations supported on structures that are randomly\nvarying in time. After settling the issue of well-posedness, we focus on the\nasymptotic behavior of solutions: our main result gives sufficient conditions\nfor pathwise convergence in norm of the (random) propagator towards a\n(deterministic) steady state. We apply our findings in two environments with\nrandomly evolving features: ensembles of difference operators on combinatorial\ngraphs, or else of differential operators on metric graphs.\n