RandGraph

Sofía from Colombia

Sofia Garzon, BMS Phase II Student, MSc Freie Universität Berlin, BSc Universidad de Los Andes, Bogotá

Martha from Uganda

Martha Nansubuga, BMS Phase II Student, MSc Humboldt University of Berlin, MSc University of Dar es Salaam (UDSM) Under...

Sophia from the US

Sophia Elia, BMS Phase II Student, BMS Qualifying Exam, Msc FU Berlin, BA UC Berkeley, California

Li Li from China

Li Li, BMS Phase II Student, BMS Qualifying Exam, Msc HU Berlin, BSc Tsinghua University

Ángel from Spain

Ángel Crespo Blanco, BMS Phase I Student, BSc University of Oviedo

Yoanna from Bulgaria

Yoanna Kirilova, BMS Phase I Student, BA Humboldt-Universität zu Berlin

Abhinav from India

Abhinav Jha, BMS Phase II Student, MSc IIT Roorkee, BSc University of Delhi

Dragana from Serbia

Dragana Radojičić, BMS Alumna, MSc TU Berlin, Qualifying Exam BMS, BSc University of Belgrade

Lena from Germany

Lena Walter, Phase II student, MSc Goethe Universität, Frankfurt

Alexander from the United Kingdom

Alexander Fairley, BMS Phase II student,Qualifying Exam BMS, BSc University of Glasgow

Simona from Bulgaria

Simona Boyadzhiyska, BMS Phase I Student, BA Wellesley College

Efstathia from Greece

Efstathia Katsigianni, BMS Phase II Student, MSc HU Berlin, Qualifying Exam BMS, BSc University of Patras

Evgenia from Russia

Evgenia Youett, BMS Phase II Student, MSc Saint Petersburg State University

Christoph from Germany

Christoph Gorgulla, BMS Alumnus, PhD completed in May 2018, MSc Freie Universität Berlin, BSc Freie Universität Berlin

Ignacio from Chile

Ignacio Barros, BMS Alumnus, PhD completed in June 2018, Qualifying Exam BMS, MSc Freie Universität Berlin, BSc Pontific...

Todor from Bulgaria

Todor Bilarev, BMS Phase II Student, Qualifying Exam BMS, MSc Humboldt-Universität zu Berlin, BSc Jacobs University Brem...

Giulia from Italy and the USA

Giulia Codenotti, BMS Phase II, MSc University of Pisa

Probabilistic and statistical methods for networks

21 August - 1 September 2017
(arrival 20 August, departure 1 September)
Venue: Mathematics Building of TU Berlin

The summer school will focus on probabilistic and statistical methods for networks. This is an enormously rich topic that has many connections between branches of mathematics, and applications to many other scientific disciplines. The central theme is randomness that may arise in various forms: it can be used to construct models for networks, to analyse networks using statistical methods, or as part of stochastic processes on networks. One strand of the school will consider the theory of statistical physics models on networks; another strand will develop tools of statistical inference in network data; and a third strand investigates applications such as networks in neuroscience, traffic and telecommunication.

The School is primarily aimed at graduate students, but also to postdocs, working in applied probability or in one of the application fields with strong probabilistic flavour.

Speakers of minicourses

Click for a summary, suggested reading, and talk slides

Shankar Bhamidi (North Carolina) - Probabilistic and statistical problems pertaining to dynamic networks

The last few years have witnessed an explosion in the amount of empirical data on real networks motivating an array of mathematical models for the evolution of such networks. Examples range from biological networks (brain networks of interacting neurons), information transmission (Internet), transportation, social networks and swarm intelligence and the evolution of self-organized behavior through the interactions of simple agents. This has stimulated vigorous activity in a multitude of fields, including biology, statistical physics, statistics, mathematics and computer science to understand these models and quantify their predictions and relevance to real systems.

The aim of this course is to introduce junior researchers to one corner of this vast field, Dynamic networks: systems that evolve over time through probabilistic rules. The following two main themes will be pursued:

Emergence of macroscopic connectivity [2 lectures]: The first two lectures will delve into techniques for understanding how macroscopic connectivity in the network arises via microscopic interactions between agents in the network. We will consider various random graph models and study the nature of emergence of the giant component, in particular establishing sufficient conditions for these objects to belong to the same universality class as governed by Aldous's multiplicative coalescent. We will show how these techniques can be used to study not just sizes of maximal components in the critical regime but also show that the maximal components appropriately scaled converge to limiting random metric spaces.
Evolving networks and continuous time branching [1 lecture]: The last lecture will study the so-called preferential attachment family of network models emphasizing one particular technical tool: continuous time branching processes. We will show how this technique leads to rigorous asymptotic descriptions to a number of problems in the statistical modeling of real world systems ranging from Twitter event networks to change point detection in evolving networks.

Introductory reading:
"Branching process with Biological applications" by Peter Jagers.

"On the convergence of supercritical general (C-M-J) branching processes" by Nerman.
https://link.springer.com/article/10.1007/BF00534830

"Brownian excursions, critical random graphs and the multiplicative coalescent" by Aldous.
https://projecteuclid.org/euclid.aop/1024404421

Durrett: https://services.math.duke.edu/~rtd/RGD/RGD.pdf

van der Hofstad: http://www.win.tue.nl/~rhofstad/NotesRGCN.pdf

Advanced reading:
"Scaling limits of critical random graphs" by Addario-Berry, Broutin and Goldschmidt.
https://projecteuclid.org/euclid.ejp/1464819810

"Universality for critical random graphs": https://arxiv.org/abs/1411.3417

"Twitter event networks and the Superstar model":
http://projecteuclid.org/euclid.aoap/1438261046

"Spectra of large random trees":
https://link.springer.com/article/10.1007/s10959-011-0360-9

Lecture 1
Lecture 1 worksheet
Lecture 2
Lecture 2 worksheet
Lecture 3

Benedikt Jahnel (Berlin) - Stochastic geometry in telecommunications

Lecture
Exercise

Max Klimm (Berlin) - Selfish routing in networks

Lecture
Exercises
Solutions

Peter Mörters (Cologne) - Reinforced branching processes

Lecture
Exercise

Tiago Peixoto (Bath) - Statistical inference of network structure and dynamics

Lecture 1
Lecture 2

Jörg Polzehl (Berlin) - Connectivity networks in neuroscience - construction and analysis

Lecture

Wilhelm Stannat (Berlin) - Stochastic mean-field theories for brain networks

Lecture

Lenka Zdeborová (Saclay) - Inference on networks via cavity method and message passing

Lecture
Lecture notes

Talks by Organisers:

Talks by Participants:

The schedule and further information.

Please direct scientific questions about the school to the organisers:

This email address is being protected from spambots. You need JavaScript enabled to view it.
This email address is being protected from spambots. You need JavaScript enabled to view it.
This email address is being protected from spambots. You need JavaScript enabled to view it.
This email address is being protected from spambots. You need JavaScript enabled to view it.
This email address is being protected from spambots. You need JavaScript enabled to view it.

and administrative questions to This email address is being protected from spambots. You need JavaScript enabled to view it..

Summer School 2017:

Probabilistic and statistical methods for networks

Speakers of minicourses

Probabilistic and statistical problems pertaining to dynamic networks

Stochastic geometry in telecommunications

Selfish routing in networks

Reinforced branching processes

Statistical inference of network structure and dynamics

Connectivity networks in neuroscience - construction and analysis

Inference on networks via cavity method and message passing

Talks by Organisers:

Talks by Participants: