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We analyze the random sequential dynamics of a message passing algorithm for Ising models with random interactions in the large system limit. We derive exact results for the two-time correlation functions and the speed of convergence. The {em de Almedia-Thouless} stability criterion of the static problem is found to be necessary and sufficient for the global convergence of the random sequential dynamics.
Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to desc
Approximate message passing algorithms proved to be extremely effective in reconstructing sparse signals from a small number of incoherent linear measurements. Extensive numerical experiments further showed that their dynamics is accurately tracked b
We construct and solve a classical percolation model with a phase transition that we argue acts as a proxy for the quantum many-body localisation transition. The classical model is defined on a graph in the Fock space of a disordered, interacting qua
The Vicsek fractals are one of the most interesting classes of fractals and the study of their structural properties is important. In this paper, the exact formula for the mean geodesic distance of Vicsek fractals is found. The quantity is computed p
We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their quantum phase transition driven by the anisotropy and dimerization, respectively. Using exact expressions for magnetization, correlation functions and energy gap, obtained by