Evrydiki Nestoridi
Stony Brook University, NY·Mathematics & Statistics
How many times must you shuffle a deck of cards before it is truly random? Questions like this are about Markov chains.
- Fields
Mathematics & Statistics
Computer Science
Physics
- Topics
Markov chains
mixing times
cutoff phenomenon
- Grants
- 1 known grant, through Jun 2027
What they work on
- Develop versatile techniques for bounding mixing times, the time a Markov chain takes to reach equilibrium, across particle systems, random walks on groups and card shuffles.
- Establish when the cutoff phenomenon occurs, an abrupt drop in a chain's distance from equilibrium, using representation theory, combinatorics and probability.
- Determine limit profiles, the exact shape of convergence to equilibrium as system size grows, for important Markov chains.
- Analyze mixing in exclusion processes, particle systems where particles cannot share a site, which model traffic congestion and gas molecule motion.
More about the research
These are random processes that move step by step between states, and they are used to generate random objects such as colorings of graphs or triangulations of a polygon. Markov chains underlie sampling and approximate-counting algorithms in computer science, statistical physics and cryptography. Card shuffles even connect to DNA rearrangements in biology. A central question is the mixing time: how long a chain takes to reach equilibrium.
Why it matters
Sharper estimates of how fast random processes mix tell algorithm designers how long sampling and counting algorithms must run. These algorithms are used in computer science, cryptography and statistical physics. The results could also inform models of traffic, gas molecules and DNA rearrangement.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Cesar Cuenca
Ohio State University, OH·Mathematics & Statistics
Describe the large-scale behavior of continuous and discrete beta-ensembles (Boltzmann distributions generalizing random matrix eigenvalues and random partitions) at different temperature limits, using new versions of free probability.
Do Young Eun
North Carolina State University, NC·Computer Science
Design self-repellent random walks, multiple interacting walkers that avoid their collective history, with adaptive repellency across space and time to maximize sampling efficiency, and prove theoretical performance guarantees.
Amir Dembo
Stanford University, CA·Mathematics & Statistics
Characterize the limiting behavior of large sparse random graphs, such as Erdős–Rényi graphs, through explicit variational formulas that do not depend on model details.
The school
Stony Brook University: 32 labs on PI Pages, $319M a year on research, 289 research doctorates a year.
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