We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems 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 novel features of the particle systems is the presence of spatial inhomogeneity which can lead to the formation of traffic jams.
8-10 • Moscow, Russia • Conference “New Frontiers in Representation Theory” dedicated to the 70th birthday of G.I.Olshanski, at SkolTech Center for Advances Studies
31-1 • Minneapolis, MN • University of Minnesota
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:
lpetrov.cc
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.
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.
This talk describes results on continuous space TASEP in inhomogeneous space, based on papers with Borodin and with with Knizel and Saenz, and on some work in progress.
This sign works equally well for both $q$-Bosons and $t$-Bosons, so the choice of parameter is up to the tourist.
T. Sasamoto and M. Wadati, Exact results for one-dimensional totally asymmetric diffusion models, J. Phys. A 31 (1998), 6057–6071
A. Borodin, I. Corwin, L. Petrov, T. Sasamoto, Spectral theory for the q- Boson particle system, Compositio Mathematica 151 (2015), no. 1, 1–67, arXiv:1308.3475 [math-ph]