This workshop aims to introduce Ph.D. students and researchers in electrical engineering, computer science, operations research and applied probability to some of the major themes at the forefront of research in applied probability which have serious implications to engineering sciences. These include information theoretic inequalities, rumour, consensus and epidemics on networks, anti-concentration inequalities, and random graphs. There will be four short courses in these topics by leading researchers in India and abroad, supplemented by tutorials. The objective is to give a rapid exposure to some cutting edge themes in these areas for those who may want to use them in their own research. A good grounding in probability theory is required.
Syllabus to be covered in terms of modules of 6 lectures each :
|
Name of the Speaker with affiliation, who will cover each module of 6 lectures. |
No. of Lectures |
Detailed Syllabus |
|
Prof. V. Anantharam, Dept. of Elec. Engg. and Computer Sci., Uni. of California, Berkeley, USA |
5 |
Title: Information theoretic inequalities Abstract: 1. Basic information-theory and associated inequalities 2. Inequalities centering around subadditivity 3. Entropy power inequalities 4. Strong data processing inequalities and hypercontractivity 5. Optimal transport and HWI inequalities. |
|
Prof. Antar Bandyopadhyay, Stat-Math Unit, Indian Statistical Institute, New Delhi |
5 |
Title: Random Graphs 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:
|
|
Prof. Krishanu Maulik ISI Delhi |
5 |
Title: Urn Models. Abstract: The course will provide an introduction to urn models. We shall start with the classical Polya urn and its analysis. We shall then consider different variants of the replacement matrices, including the cases where we allow withdrawal of balls from the urn, and study some examples. We shall then consider replacement matrices with nonnegative entries only. We shall analyze such matrices first using martingale methods under the added assumption that the row sums are same. Next we shall study such matrices in general by embedding the urn process into a continuous time branching process using Athreya-Karlin embedding. |
|
Prof. Manjunath Krishnapur, Dept. of Mathematics, Indian Institute of Science, Bangalore |
5 |
Title: Anti-concentration inequalities. Abstract: We give an exposition of basic anti-concentrtion inequalities for sums of independent random variables. Starting from results of Littlewood and Offord and Edros, on to those of Kolmogorov and Rogozin and then to more recent results of Rudelson and Vershynin and of Tao and Vu, we intend to give a survey along with proofs. In the end we discuss certain relative anti-concentration inequalities. Applications of these inequalities to random matrices and randon polynomials will be given. The lectures should be understandable to anyone who has taken a graduate level course in probability (in particular, characteristics functions and their properties). |
Names of the tutors :
1. Prof. V. S. Borkar, EE, IIT Bombay.
2. Prof. Rajesh Sundareshan, ECE, IISc Bangalore.
|
Day |
Date |
Lecture 1 9.30–10.30 |
Tea 10.35
|
Lecture 2 11.00–12.00 |
Lecture 3 12.15 – 1.15 |
Lunch 1.15–2.30
|
Lecture 4 2.30-3.30 |
Tea 3.35
|
Tutorial/ Discussion 4.00-5.00 |
Tea/ Snacks 5.05-5.30
|
|
|
2016 |
(name of the speaker) |
(name of the speaker ) |
(name of the speaker) |
(name of the speaker) |
(Names of the tutors) |
||||
|
Mon |
4 Jan |
Antar |
Manju |
Ananth |
Krishanu |
Borkar |
||||
|
Tues |
5 Jan |
Antar |
Manju |
Ananth |
Krishanu |
Rajesh |
||||
|
Wed |
6 Jan |
Antar |
Manju |
Ananth |
Krishanu |
Rajesh |
||||
|
Thu |
7 Jan |
Antar |
Manju |
Ananth |
Krishanu |
Borkar |
||||
|
Fri |
8 Jan |
Antar |
Manju |
Ananth |
Krishanu |
Rajesh |