+91-674-249-4082

Submitted by nabinjana on 5 September, 2017 - 17:10

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.

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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