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Syllabus

We will examine different spatial random graphs models with applications to communications. In these models nodes are connected toghether depending on their relative positions in the plane, and form a graph whose structure depends on their random position. Such models have attracted the attention in recent years of mathematicians, engineers, and computer scientist, due to their ability to describe real networks, including devices sending data over wireless. Specific topics include discrete percolation, continuum percolation, models with interference. Connectivity, capacity, delay, and information theoretic implications. Students will also be introduced to a number of open research problems.

Policy

Homeworks are not graded, the class grade will be based on presentation of research papers in class.

Homeworks

Homework 1.

Homework 2.

Homework 3.

Homework 4.

Study Groups

Groups and schedule of research papers will appear here.

Some References

Grimmett. Percolation, Springer. (Discrete percolation models)
Meester and Roy. Continuum Percolation, Cambridge. (Continuum models).
Phase Transitions.
(Discrete percolation). S. R. Broadbent, J. M. Hammersley (1957). Percolation processes I. Crystals and mazes.
Proceedings of the Cambridge Philosophical Society, 53, 629--641.
(Nearest neighbors). O. Haggstrom, R. Meester (1996). Nearest neighbor and hard sphere models in continuum percolation.
Random structures and algorithms 9(3), 295--315.
(Boolean model). E. N. Gilbert (1961). Random plane networks.
Journal of SIAM 9, 533--543.
(Random Connection Model). M. D. Penrose (1991). On a continuum percolation model.
Advances in Applied Probability 23(3), 536--556.
(Interference limited networks). O. Dousse, F. Baccelli, P. Thiran. Impact of interferences on connectivity in ad-hoc networks.
IEEE/ACM Transactions on Networking, INFOCOM 2003.