[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.

Workshop on Representation Theory, Combinatorics, and Geometry
will be at University of Virginia on **October 19-21, 2018**. The workshop precedes
the Virginia Mathematics Lectures by Andrei Okounkov (October 22-24)

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

[Fall 2018 semester]

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

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

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

[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:

- this homepage
`lpetrov.cc`

- the FRG website
- the UVA Math department website

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.

[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.