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Abstract
摘要 |
Computing the marginal probabilities of a Gibbs-Boltzmann probability distribution has many applications in Physics and outside Physics. Efficient approximate methods have been developed over several decades to achieve this task if the graph of interactions has a locally tree-like form, as it has for random graphs. In Physics these methods are called the cavity method or the Bethe-Peierls method; in computer science they are called Belief Propagation and in Information Theory they are a part of iterative decoding.
It is an open issue whether similar methods could also be competitive to determine the marginals of the probability distributions of non-equilibrium Physics, e.g. for the dynamics on random graphs. The case of exclusively one-way interactions (fully assymmetric couplings) was studied by Derrida and co-workers already more than 20 years ago, but is obviously special. We and others have over the last five years studied a version of this problem called the dynamic cavity and showed that it works well for the discrete-time (parallel update) kinetic Ising model on a random graph with partly symmetric and partly assymmetric, though, sufficiently weak, couplings (high-temperature regime).
In this talk I will describe recent progress on the continuous-time version of this problem. The talk is based on: Erik Aurell, Gino Del Ferraro, Eduardo Dominguez, Roberto Mulet, ``A Cavity Master Equation for the continuous time dynamics of discrete spins models" [arXiv:1607.06959] (2016) |
