Limit shapes in the discrete model interpolating out from the geometric corner growth

Generalizations of TASEP in discrete and continuous inhomogeneous space

[2018/08/29]

We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems evolve in discrete or continuous space and can be thought of as new exactly solvable examples of tandem queues, directed first- or last-passage percolation models, or Robinson-Schensted-Knuth type systems with random input. One of the features of the particle systems we consider is the presence of spatial inhomogeneity which can lead to the formation of traffic jams.

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Simulation of the six vertex model with domain wall boundary conditions and gaseous phase (simulation due to Shreyas Balaji)

Virginia Integrable Probability Summer School

Virginia Integrable Probability Summer School will be held at University of Virginia from May 27 to June 8, 2019 (details will be added soon)

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Front of percolation

MATH 3100 • Introduction to Probability (2 sections)

[Fall 2018 semester]

2019 travel

January

8-10 • Moscow, Russia • Conference at SkolTech Center for Advances Studies

March

10-15 • Banff, Alberta, Canada • BIRS Workshop “Asymptotic Algebraic Combinatorics”

May

13-14 • Durham, NC • SouthEastern Probability Conference 2019

All 2019 travel »

[quick link] My big BiBTeX file

How to enable SSL for a homepage hosted on S3

[2018/04/13]

As Google Chrome will mark all HTTP websites unsafe later this year, it is time to figure out how to enable SSL on my websites. I currently have 3 websites under active management:

All three of them are hosted through AWS, but the homepage is by far the easiest as it only involves S3 and no EC2 instances. So at first I decided to turn on SSL at the homepage, which I succeeded with.

Steps and some caveats »

A histogram of the path energies ‐ the original motivation for the work

Quenched Central Limit Theorem in a Corner Growth Setting

[2018/04/12]

We consider point-to-point directed paths in a random environment on the two-dimensional integer lattice. For a general independent environment under mild assumptions we show that the quenched energy of a typical path satisfies a central limit theorem as the mesh of the lattice goes to zero. Our proofs rely on concentration of measure techniques and some combinatorial bounds on families of paths.

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