This course will provide an introduction to and some analysis of the main mathematical models used to describe large networks and dynamical processes that evolve on networks. Motivation and applications will be drawn from social, economic, natural, and infrastructure networks, as well as networked decision systems such as sensor networks.

It is designed for an audience of Ph.D. students with some mathematical background (in particular, probability and linear algebra at an intermediate level), possibly from the programs in Automatic Control, Electrical Engineering, Computer Science, Mathematics, Mathematical Statistics, Physics, ...

The first lecture is scheduled on Tuesday, October 1, 2013, at 13:15-15:00 in the seminar room M:2498 of the Automatic Control Department. (on the second floor in the M-building)

The course will then continue in October and November with nine more lectures (tentatively on Wednesdays 10:15-12:00) and eight exercise sessions (tentatively on Tuedays 13:15-15:00): if possible, we will try to accommodate specific time constraints. The last exercise session and lecture may be postponed from the last week of November to the first week of December.

The course will be worth 9 credits. To be granted such credits, students will be have to do the homework assignments (tentatively 8 sheets, assigned on a weekly basis) as well as some final reading and presentation/discussion (to be arranged with the lecturer on an individual basis).

A tentative syllabus is available here.

For any information, please contact the lecturer giacomo.como@control.lth.se

Homeworks:

**Homework 1, **due on Tue, Oct 8

**Homework 2, **due on Tue, Oct 15

**Homework 3, **due on Tue, Oct 22

**Homework 4, **due on Tue, Oct 29

** Homework 5, **due on Tue, Nov 5

**Homework 6, **due on Tue, Nov 12

**Homework 7, **due on Tue, Nov 19

**Homework 8, **due on Tue, Nov 26

Material:

Lecture 0 (Tue, Oct 1): Introduction

**Slides** of the lecture (do not print them if you care about toner!)

**Introductory survey article** by Mark Newman from SIAM review (sort of anchestor of his book)

Lectures 1 and 2 (Wed, Oct 2 and 9): Random walks and Markov chains

Some **notes**

**Survey article** by Lovasz

**Textbook** (very accessible) on Markov chains by Levin, Peres, and Wilmer

**Monograph** (more advanced) by Aldous and Fill

**Monograph** (more advanced) by Montenegro and Tetali

Lectures 3 and 4 (Wed, Oct 16 and 23): Averaging and the voter model

Some **notes **will come here

In the meanwhile, you can refer to chapter 6.9 of Durrett, Random Graph Dynamics, Cambridge University Press, 2007, for an introduction to the voter model; to this paper for an introduction to the averaging model; to this survey for an introduction to gossip algorithms; and to this paper for the versions with stubborn agents.

Lectures 5 and 6 (Wed, Oct 30 and Nov 6): Mean-field limits

Some **notes **will come here

In the meanwhile, you can refer to Chapter 5 of Draief and Massoulié, Epidemics and rumors in complex networks, Cambridge University Press, 2010, a preliminary version of which is **this one** (where the relevant chapter is the first one)

Lectures 6 and 7 (Wed, Nov 6 and 13): Branching process

Some **notes **will come here

In the meanwhile, you can refer to Chapter 2.1 of Durrett, Random Graph Dynamics, Cambridge University Press, 2007, as well as to Chapter 1 of Draief and Massoulié, Epidemics and rumors in complex networks, Cambridge University Press, 2010.

Lecture 7 (Wed, Nov 13): Erdos-Renyi random graph, configuration model, epidemics

Some **notes **will come here

In the meanwhile, you can refer to Chapters 2.2, 3.1, and 3.5 of Durrett, Random Graph Dynamics, Cambridge University Press, 2007, as well as to Chapter 2 of Draief and Massoulié, Epidemics and rumors in complex networks, Cambridge University Press, 2010.

Lecture 8 (Wed, Nov 20):

Lecture 9 (Wed, Nov 27):