Duke Probability Seminar
A seminar for the probability community at Duke, both in and outside of the Mathematics Department.
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- Thursday, April 6, 2017, 3:15pm, 119 Physics, Probability Seminar
Coupling, geometry and hypoellipticity
Sayan Banerjee (UNC)
- Thursday, April 20, 2017, 4:15pm, UNC, 125 Hanes Hall, Probability Seminar
Latent voter model on locally tree-like random graphs
Rick Durrett (Duke)
- In the latent voter model, which models the spread of a technology through a social network, individuals who have just changed their choice have a latent period, which is exponential with rate λ during which they will not buy a new device. We study site and edge versions of this model on random graphs generated by a configuration model in which the degrees d(x) have 3 ≤ d(x) ≤ M. We show that if the number of vertices n → ∞ and log n << λn << n then the latent voter model has a quasi-stationary state in which each opinion has probability ≈ 1/2 and persists in this state for a time that is ≥ nm for any m <∞. Thus, even a very small latent period drastically changes the behavior of the voter model.
- Thursday, April 27, 2017, 4:15pm, UNC, 125 Hanes Hall, Probability Seminar
A Dirichlet Form approach to MCMC Optimal Scaling
Wilfrid Kendall (U of Warwick)
- In this talk I will discuss the use of Dirichlet forms to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis-Hastings random walk samplers) under regularity conditions which are substantially weaker than those required by the original approach (based on the use of infinitesimal generators). The Dirichlet form method has the added advantage of providing an explicit construction of the underlying infinite-dimensional context. In particular, this enables us directly to establish weak convergence to the relevant infinite-dimensional diffusion.
Zanella, G., Kendall, W. S., & Bédard, M. (2016). A Dirichlet Form
approach to MCMC Optimal Scaling.
arXiv, 1606.01528, 22pp. URL: arxiv.org/abs/1606.01528
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