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High-dimensional estimation with geometric constraints
A general model where it is only assumed that each observation y_i may depend on a_i only through , which leads to the intriguing conclusion that in the high noise regime, an unknown non-linearity in the observations does not significantly reduce one's ability to determine the signal, even when the non- linearity may be non-invertible.
Systems with large flexible server pools: Instability of “natural” load balancing
We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed…
Tightness of Invariant Distributions of a Large-scale Flexible Service System Under a Priority Discipline
indexing the systems by parameter r, it is shown that the system under LAP discipline is stochastically stable for all sufficiently large r and the family of the invariant distributions is tight on scales r12+𝜖 for...
Continuous time Markov processes
This article provides the mathematical foundation for the often used continuous time Monte Carlo simulation.
A compact, highly-motivated introduction to some of the stochastic models found useful in the study of communications networks.
Introduction to Representation Theory
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to…
Matrix-Ball Construction of affine Robinson–Schensted correspondence
- Michael Chmutov, P. Pylyavskyy, E. Yudovina
- MathematicsDiscrete Mathematics & Theoretical Computer…
- 18 November 2015
In his study of Kazhdan–Lusztig cells in affine type A, Shi has introduced an affine analog of Robinson–Schensted correspondence. We generalize the Matrix-Ball Construction of Viennot and Fulton to…
A Markov Model of a Limit Order Book: Thresholds, Recurrence, and Trading Strategies
This work analyzes a tractable model of a limit order book on short time scales, and establishes the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresholds.
Generalized continued fractions and orbits under the action of Hecke triangle groups
1. Background. The Hecke triangle groups G(λ) are the groups of fractional linear transformations generated by the transformations S(z) = z + λ and T (z) = −1/z. Hecke  showed that these groups…
Socially Optimal Charging Strategies for Electric Vehicles
This paper studies decentralized policies that assign electric vehicles to a network of charging stations with the goal to achieve little to no queueing, and provides insight into the optimal location deployment of the charging infrastructure.