in Advanced Probability
August 18-21, 2016, Novosibirsk, Russian Federation
The School is associated with the VIth Conference "Modern Problems in Theoretical and Applied Probability". Its aim is to facilitate communication among participants, and to provide an in-depth introduction to the field of probability theory. The School is intended for undergraduate and PhD students interested in probability theory, statistics, and applications of these techniques.
The School's working language is English.
All participants are encouraged to make a poster presentation about their research work during the evening scientific session of the School.
In this minicourse we look at a class of stochastic processes with reinforcement, which includes urn models, preferential attachment networks with fitness, and genetic house-of-cards models. These processes can be described in terms of a class of general branching processes, often called Crump-Mode-Jagers processes. In the first part of the course I will explain the classical convergence theory of these processes under the assumption of existence of a Malthusian parameter. We will explore when this assumption is satisfied in our examples. In the second part I will present recent research (joint with Steffen Dereich and Cecile Mailler) exploring the interesting phenomena that may occur if this assumption fails.
Many problems of interest in computer science, information theory and statistics can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large graph. In recent years, considerable progress has been achieved by viewing these distributions as Gibbs measures and applying to their study heuristic tools from statistical physics. In this course, we will review this approach and provide some results towards a rigorous treatment of these problems.
|Novosibirsk State University||Sobolev Institute of Mathematics||Siberian Branch of RAS|