News & Events

SLSM

Date/Time: 
Monday, October 9, 2017 - 11:30 to 13:00
Venue: 
SMS Seminar Room
Speaker: 
Antar Bandyopadhyay
Affiliation: 
Indian Statistical Institute, New Delhi
Title: 
Random Graphs

This is a Short Lecture Series in Mathematics (SLSM) consisting of 4 lectures of 90 minutes each. This lecture schedule in this series is the following:

1st Lecture: Monday, October 09, 2017 - 11:30 to 13:00

2nd Lecture: Tuesday, October 10, 2017 - 11:30 to 13:00

3rd Lecture: Wednesday, October 11, 2017 - 16:30 to 18:00

4th Lecture: Thursday, October 12, 2017 - 15:30 to 17:00

Abstract: The first half of the mini course will be an introducing to the two classical models of random graphs (a.k.a. Erdős-Rényi random graphs) and discuss the phenomenon of phase transition. We will also discuss thresholds for monotonic properties with examples including connectivity threshold and sub-graph containment threshold.

In the second half of the course we will consider other kind of random graphs. In particular, we will discuss various models for complex networks, including Albert-Barabási preferential attachment models. We will discuss "scale-freeness", asymptotic degree distribution and "small-world phenomenon". Properties of super and sub-linear preferential attachment models and some recent developments in de-preferential attachment models will also be discussed.

If time permits we will also introduce the random geometric graphs and discuss asymptotic of the connectivity threshold.

 

References:

   1. Random Graphs by Svante Janson, Tomasz Łuczak and Andrzej Rucinski;
   2. Random Graphs by Béla Bollobás; 
   3. Random Graphs and Complex Networks by Remco van den Hofstad;
   4. Random Geometric Graphs by Mathew Penrose. 

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