Abstract:
We consider a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings: (I) the random environment is resampled at every unit of time; (II) the random environment is sampled at time zero only. In our model the random environment is resampled along an increasing sequence of deterministic times. We consider both the quenched and the annealed version of the model, and look at various growth regimes for the resampling times. We prove laws of large numbers, central limit theorems and large deviation principles. We also look at classification of transience versus recurrence. Joint work with Luca Avena, Yuki Chino and Conrado da Costa.
Biography:
Frank received his Ph.D. at Leiden University in 1985, under the supervision of Piet Kasteleyn. Since then he has worked at the universities of Delft, Utrecht, Nijmegen and Eindhoven. He is currently Full Professor of probability theory at Leiden University.
Frank works in probability theory, statistical physics, ergodic theory, population genetics and complex networks. His main focus has been on interacting particle systems, phase transitions and disordered media.
Frank has received multiple grants from the Netherlands Organisation for scientific research, as well as an advanced grant from the European Research Council. He is also one of the Principle Investigators of the Dutch Gravitation program NETWORKS, a collaboration between researchers from Amsterdam, Leiden and Eindhoven that combines stochastics and algorithmics to solve network problems.
Frank was elected to the Royal Netherlands Academy of Arts and Sciences in 2005. In 2016 he became Knight in the Order of the Dutch Lion. In 2018 he received a Humboldt Research Award.
Frank has been Visiting Professor in Bonn, Erlangen, Göttingen, Heidelberg, Toronto and Vancouver. He has served on many national and international advisory boards. He is currently chair of the Advisory Council for the Natural and Technical Sciences of the Royal Netherlands Academy of Arts and Sciences.
He has lectured at conferences, workshops and summer school around the world, and co-organised 55 national and international workshops. He is the author of 170 research papers and 3 monographs. He has supervised 22 Ph.D. students and 34 postdocs.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai