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Distributed average consensus with least-mean-square deviation
Distributed average consensus Least-mean-square Convex optimization Edge-transitive graphs
2015/8/10
We consider a stochastic model for distributed average consensus, which arises in applications such as load balancing for parallel processors, distributed coordination of mobile autonomous agents, and...
Asymptotics of the Invariant Measure in Mean Field Models with Jumps
decoupling approximation fluid limit invariant measure McKean-Vlasov equation mean field limit small noise limit
2011/9/16
Abstract: We consider the asymptotics of the invariant measure for the process of the spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects th...
A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics
critical mean-field Swendsen-Wang dynamics Probability
2011/9/9
Abstract: The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the com...
Weak disorder in the stochastic mean-field model of distance II
First passage percolation complete graph extreme value theory hopcount
2010/12/9
In this paper, we study the complete graph Kn with n vertices, where we attach an i.i.d. weight to each of the n(n − 1)/2 edges. We focus on the weight Wn and the number of edges Hn of the minim...
Stochastic Mean-Field Limit: Non-Lipschitz Forces \& Swarming
Mean-field limit diffusion Cucker-Smale collective behavior
2010/12/13
We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the sy...
Optimal coupling for mean field limits
Mean field limits transportation inequalities concentration inequalities optimal coupling
2010/12/9
We review recent quantitative results on the approximation of mean field dif-fusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a l...