This week

The graphical construction of the asymmetric simple exclusion process (ASEP) provides a coupling to a common iid Poissonian environment of the evolution of any initial data started at any time. I will describe how the scaling limit of this coupled evolution over all initial data and starting times is given in terms of variational problems involving the directed landscape. I will then explain how the Yang-Baxter equation and machinery of Gibbsian line ensembles provides a systematic route to extract this limit, as well as that of any model in Integrable Probability.

The workshop will focus on mathematical modelling and computational techniques for renewable energy systems and markets.

SMC (Sequential Monte Carlo) samplers are a class of iterative algorithms that generate Monte Carlo approximations on a sequence of target distributions. They may be used either in genuine sequential scenarios (i.e. for on-line learning, where data are processed sequentially), or when there is only target distribution of practical interest (and then one designs an artificial sequence to interpolate between an easy-to-sample distribution and the target distribution). This talk will be based on two recent papers; one (with Hai-Dang Dau, NTU) who introduced waste-free SMC samplers as a better alternative over standard SMC samplers, and another (with Yvann Le Fay, ENSAE), where we study how the complexity (number of likelihood evaluations) of these samplers scale with respect to various aspects of the target distributions, such as the length of the sequence, the mixing times of the Markov kernels, the dimension of the ambient space, and so on. These complexity results leads to practical guidelines on how to obtain optimal performance for these algorithms, as I will argue at the end of my talk.