# PhD Position on Random Matrices for Complex Network Analysis, Inria/EURECOM, Sophia Antipolis, France

The Laboratoire d’excellence UCN@SOPHIA grants a PhD scholarship on

Random matrix analysis for distributed algorithms and complex networks

hosted at MAESTRO team, Inria and Dpt. of Wireless Communications, EURECOM

Further information at

www.eurecom.fr

and

http://www.eurecom.fr/cm/

http://www.inria.fr/centre/sophia/

and

http://www-sop.inria.fr/maestro/

*** Research topic description

The continuous growth of Internet, social networks, the quest for a deep understanding of biological and physical networks for nanotechnologies is fuelling intense researches to investigate fundamental interconnection structures and dynamics of physical and logical complex networks and gave birth to a new discipline called “Network Science”. Network Science aims to develop new theory, mathematical principles and algorithms to understand the intrinsic communication patterns, the growth and decay dynamics, as well as information propagation in such complex systems.

A complex network can be effectively modeled by random matrices. The properties of the random ensemble characterize a complex network as a whole, beyond the peculiarities of single realizations and provide macroscopic metrics and insightful topological parameters useful both in design and analysis of complex networks. Random matrix theory (RMT) is a branch of mathematics that investigates the spectral properties of random matrices. It has been successfully applied to many disciplines where complex interactions among a large number of entities play a key role. The spectra of many classes of random matrices converge to asymptotic deterministic limit as the size of the matrix grows large and the spectra can be analytically expressed in terms of few parameters. As a consequence, the properties of complex systems related to these random matrix spectra can also be expressed in terms of few macroscopic system parameters. The aim of this doctoral programme is to extend the benefits that RMT had in fields as physics and telecommunications, to complex networks and derive analytical results on the spectra of large matrices modeling complex networks. This will allow to establish fundamental relations between macroscopic parameters and topological properties of the networks.

* Some references

L. Cottatellucci, et al. “Asynchronous CDMA systems with random spreading–Part I: Fundamental limits”. IEEE Trans. on Information Theory, vol. 56, no. 4, Apr 2010.

T. Nagao, et al., Spectral density of complex networks with a finite mean degree, Journal of Physics A: Mathematical and Theoretical, 2008 41

L. Erdos, Universality of Wigner random matrices: a survey of recent results, Russ. Math. Surv. 66 507, http://arxiv.org/pdf/1004.0861.pdf

T. Tao, et al., "Random matrices: Universality of local eigenvalue statistics." Acta mathematica 206, no. 1 (2011): 127-204

***Requirements

We are looking for a highly motivated person with a master degree in mathematics, computer science, communications and information technology or related fields. The key prerequisite is excellent mathematical skill. Specialization in advanced probability theory and/or linear algebra will be considered an advantage. Relevant prerequisites are also a certain degree of independence, capability to take initiative, and good English command.

***Application File

Motivation letter, CV, academic transcripts (with explanation of the grade scale adopted), 2 references (letters or names) to

k.avrachenkov@sophia.inria.fr

laura.cottatellucci@eurecom.fr

http://www-sop.inria.fr/members/Konstantin.Avratchenkov/me.html

http://www.eurecom.fr/en/people/cottatellucci-laura

*** Diffusion Date

August 2013

***Start Date

October 2013 or later (quite flexible)

***Duration

36 months

**Submitted by Anonymous |

**14 / Aug / 2013