Due to the epidemiological situation, the content, format and schedule of the school have changed: Dr D. Fraser will start reading his lectures online at the end of April; Prof. S. Foss will continue reading his special course for NSU students. To participate in the school fill in the form.

Spring School in Advanced Probability 2020

Mathematical Center in Academgorodok, Novosibirsk State University

April 5-11, 2020, Novosibirsk, Russian Federation

Home School Programme General information
Rate-allocation in wireless communication networks: stability and throughputs

Doctor Vsevolod Shneer, Heriot-Watt University, Edinburgh

We will consider a range of models motivated by various protocols for transmitting messages in wireless communication networks. Among these protocols and the well-known MaxWeight, alpha-fair, CSMA and others. We will consider questions of stability and throughput achieved by networks governed by these protocols.

Seva Shneer is an Associate Professor at the Department of Actuarial Mathematics and Statistics at Heriot-Watt University, Edinburgh, UK. Seva received his PhD in probability from Heriot-Watt University in 2006 and later held a postdoctoral position at EURANDOM, Eindhoven University of Technology. He then worked as a senior research fellow at EPFL, Lausanne, Switzerland, before joining Heriot-Watt University as Assistant Professor in 2010. Seva's main research interests are in stability and performance analysis of stochastic networks, especially those appearing in queueing theory, communication networks, data centres and energy applications.
The Stein-Chen method: Coupling techniques for probability approximations

Doctor Fraser Daly, Heriot-Watt University, Edinburgh

The Stein-Chen method is a powerful modern technique for obtaining explicit error bounds in probability approximation, even in the presence of relatively intricate dependence between the underlying random variables. This method has its origins in the pioneering work of Charles Stein and Louis Chen in the 1960s and 70s on Gaussian and Poisson approximations, respectively, for sums of dependent random variables. Since then, the same techniques have been applied to a variety of univariate, multivariate and process-level approximations. In this course we will begin with an overview of the Stein-Chen method, focusing firstly on the classical Gaussian and Poisson cases. We will illustrate the technique with classical limit theorems and approximations for sums of locally dependent random variables. Our focus for the majority of the course will be on how coupling constructions can be applied in conjunction with the Stein-Chen method to yield explicit approximations in a variety of settings. This will include generalizations and extensions of Poisson approximation results (for example, to compound Poisson approximation), and approximation by geometric sums, with Markov chain passage times our main application here. Other examples and applications will be visited and revisited throughout the course, including approximations for runs in Bernoulli trials and for extreme values. We will also see how some of the techniques we consider may be extended to approximations on the level of stochastic processes.

Since 2013, Fraser Daly has been an assistant professor at Heriot-Watt University, UK. He previously held postdoctoral positions in Bristol and Zürich, and obtained his PhD from the University of Nottingham in 2008. His research is in applied probability, with particular emphasis on Stein's method for probability approximations and its applications in proving limit theorems for random systems and processes with dependence.
Coupling methods, updating, and perfect simulation

Professor Sergey Foss, Heriot-Watt University, Edinburgh and Novosibirsk State University, Novosibirsk

The short course includes three lectures:

Sergey Foss is a Professor at Heriot-Watt University (Edinburgh, UK), Leading Scietific Researcher at S.L.Sobolev Institute of Mathematics and Research Group Leader at Mathematical Center in Akademgorodok. Sergey’s main research interests are in stability, continuity, optimisation, and long- range dependence in stochastic processes, with applications in (tele)communications, queueing and risk.
About school

"Spring School in Advanced Probability" is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation. The school (poster) will take place at Novosibirsk State University and will consist of two 10-hour lecture courses taught in english. In addition to the courses, there will be several workshops to discuss the lectures and a poster session for students. We are happy to see participants from any university and invite them to prepare and present their own poster ( poster examples ). The Mathematical Center in Academgorodok may provide financial assistance towards travel and accommodation costs.

After our School, from the 10th to 13th of April, Novosibirsk State University hosts the traditional International Scientific Student Conference (ISSK-2020). We invite you to take part in the section "Probability theory". You can apply for participation until February 21th. For more details please visit the conference website.