# Authority on random matrix theory aims to make sense of huge data sets

##### June 27, 2014 by Helen Knight

From the increasing information transmitted through telecommunications systems to that analyzed by financial institutions or gathered by search engines and social networks, so-called "big data" is becoming a huge feature of modern life.

But to analyze all of this incoming data, we need to be able to separate the important information from the surrounding noise. This requires the use of increasingly sophisticated techniques.

Alice Guionnet, a professor of mathematics at MIT, investigates methods to make sense of huge data sets, to find the hidden correlations between apparently random pieces of information, their typical behavior, and . "I consider things called matrices, where you have an array of data," Guionnet says. "So you take some data at random, put it in a big array, and then try to understand how to analyze it, for example to subtract the noise."

The field of , as it is known, has grown rapidly over the last 10 years, thanks to the huge rise in the amount of data we produce. The theory is now used in statistics, finance, and telecommunications, as well as in biology to model connections between neurons in the brain, and in physics to simulate the radiation frequencies absorbed and emitted by heavy atoms.

Mathematics as patchwork

A world-leading researcher in probability, Guionnet has made important theoretical contributions to random matrix theory. In particular, she has made recent advances in understanding large deviations—the probability of finding unlikely events or unusual behavior within the array of data—and in connecting the theory with that of topological expansion, in which random matrices are used to help solve combinatorial questions.

"It's a bit like when you make a patchwork quilt," Guionnet says. "So you have all of your pieces of patchwork, and then you go to sew them together so that they make a nice pillow with no holes, and you have many possibilities for how to lay them out," she says.

Random matrices can be used to calculate the number of ways in which this "patchwork" can be sewn together, Guionnet says. She also considers several of these random arrays simultaneously, to help solve problems in the field of operator algebra.

Guionnet was born in Paris. She completed her master's degree at the Ecole Normale Superieure Paris in 1993, and then moved to the Universite Paris Sud to undertake her PhD. The focus of her PhD was the statistical mechanics of disordered systems, a branch of mathematical physics in which the world around us is modeled down to the level of microscopic particles. In this way, researchers attempt to determine how microscopic interactions affect activity at the macroscopic level.

In particular, Guionnet was interested in objects called spin glasses—disordered magnetic materials that are similar to real glass, in that they appear to be stationary, but which are actually moving, albeit at an incredibly slow rate. "If you looked at the windows of your house millions of years from now, they may be shifting downward as a result of gravity," she says. "I was attempting to analyze the dynamics of these kinds of systems."

Before she had completed her PhD, Guionnet was offered a position within the French National Center for Scientific Research (CNRS), and moved to Ecole Normale Superieure (ENS) Lyon, where she continued to focus on the spin glass model, before branching out into random matrices. "I initially wanted to work in applied mathematics," Guionnet says. "But as I started to consider questions in random matrix theory, I moved into purer and purer mathematics."

While at ENS Lyon, she was made a director of research for CNRS, and was given the opportunity to build her own team of top researchers in probability theory.

Making connections

She moved to MIT in 2012, where she continues her work in random matrix theory. In the same year, Guionnet was chosen as one of 21 mathematicians, theoretical physicists, and theoretical computer scientists named as Simons Investigators. Awarded by the Simons Foundation, a private organization that aims to advance research in math and the basic sciences, Simons Investigators each receive \$100,000 annually to support their work.

"What I like about my work is that it crosses over into different fields—, operator algebra, and random matrices—and I'm trying to advance these three theories at the same time," Guionnet says. "These different fields are all merging and connecting with each other, and that is what I try to understand in my work."

The opportunity to work with people from different mathematical fields, and to learn new ideas from them, is one of the things Guionnet loves most about the subject. "When you work with people from different fields you begin to make new connections, and get a new point of view on the object you are studying, so it's kind of exciting," she says.

What's more, the math itself is always evolving and progressing, she says: "Mathematics is beautiful."

Explore further: Quantum chaos in ultracold gas discovered

## Related Stories

#### Quantum chaos in ultracold gas discovered

March 12, 2014

A team of University of Innsbruck researchers discovered that even simple systems, such as neutral atoms, can possess chaotic behavior, which can be revealed using the tools of quantum mechanics. The ground-breaking research, ...

#### Q&A: Allan Sly on probability theory and random processes

February 16, 2012

Newly awarded a 2012 Alfred P. Sloan Research Fellowship, Allan Sly, assistant professor of statistics, talks about his research into probability theory, his students and his own days as a UC Berkeley graduate student.

#### New technique allows simulation of noncrystalline materials

June 22, 2012

A multidisciplinary team of researchers at MIT and in Spain has found a new mathematical approach to simulating the electronic behavior of noncrystalline materials, which may eventually play an important part in new devices ...

#### Researchers devise method to study network resistance to random failures based on 'random walks'

May 27, 2014

(Phys.org) —A small team of mathematicians with Universitat Rovira i Virgili in Spain, has come up with a way to study a network's resistance to failure. In their paper published in Proceedings of the National Academy of ...

#### Mathematicians trace source of Rogers-Ramanujan identities, find algebraic gold

April 29, 2014

Mathematicians have found a framework for the celebrated Rogers-Ramanujan identities and their arithmetic properties, solving another long-standing mystery stemming from the work of Indian math genius Srinivasa Ramanujan.

#### Discovery could lead to more difficult Sudoku puzzles

February 13, 2010

(PhysOrg.com) -- A new analysis of number randomness in Sudoku matrices could lead to the development of more difficult and multi-dimensional Sudoku puzzles. In a recent study, mathematicians have found that the way that ...

## Recommended for you

#### Ancient burials suggestive of blood feuds

October 24, 2016

There is significant variation in how different cultures over time have dealt with the dead. Yet, at a very basic level, funerals in the Sonoran Desert thousands of years ago were similar to what they are today. Bodies of ...

#### Dinosaurs of a feather flock and die together?

October 24, 2016

In the paleontology popularity contest, studying the social life of dinosaurs is on the rise.

#### Model helps explore how changing certainty in belief of one statement can lead to changings belief in truth of others

October 21, 2016

A small team of researchers with members from the U.S., the Netherlands, Russia and Italy has developed a new model that illuminates how changing the degree of certainty a person holds for a given belief can lead to changes ...

#### Science sheds light on 250-year-old literary controversy

October 21, 2016

The social networks behind one of the most famous literary controversies of all time have been uncovered using modern networks science.

#### Meet Savannasaurus, Australia's newest titanosaur

October 21, 2016

The outback region around Winton in central Queensland is arguably Australia's ground zero for giant dinosaur fossils. Here, graziers occasionally stumble across petrified bones on their paddocks, amid the stubbly grass and ...

#### A weird combination of Deinotherium and Platybelodon- Elephantiformes without ivories

October 21, 2016

In the main Proboscidean taxon of Elephantiformes, a huge pair of developed top incisors (ivories) has become a distinctive feature of this taxon. The structure is usually made as a tool for individual foraging and a weapon ...