[2017/12/17]

I’ve done some simulations of a multilayer version of the pushTASEP in inhomogeneous space, in my new simulations gallery.

Technical details and more pictures are here.

[2017/12/13]

Employing bijectivisation of summation identities, we introduce local stochastic moves based on the Yang-Baxter equation for . Combining these moves leads to a new object which we call the spin Hall-Littlewood Yang-Baxter field - a probability distribution on two-dimensional arrays of particle configurations on the discrete line. We identify joint distributions along down-right paths in the Yang-Baxter field with spin Hall-Littlewood processes, a generalization of Schur processes. We consider various degenerations of the Yang-Baxter field leading to new dynamic versions of the stochastic six vertex model and of the Asymmetric Simple Exclusion Process.

Updated gallery of simulations of integrable stochastic systems

[2017/12/12]

Doing bibliography with BiBLaTeX (and having one huge `.bib`

file - mine is public, by the way)
works great for me.

One downside is that arXiv uses a specific TeXLive
distribution (2016 as of today), and the distribution on my machine is more up to date.
Also, arXiv wants `.bbl`

files uploaded instead of huge `.bib`

files
(`.bbl`

contains only the references actually included in a given paper, and not all over 900 references which are in my `.bib`

file).
The problem is that `.bbl`

files produced by different versions of BiBLaTeX are incompatible (!).
So, to upload a paper to arXiv, I need to install a version of TeXLive identical to the arXiv’s one.

[2017/12/12]

I produce almost all pictures in my math writing in TikZ. This is a nice library (and I’ve learned it over the years), which allows for-loops, effects, etc. The downside for me always was that compiling inline TikZ pictures takes a lot of time. For some months now, while writing a particularly figure-heavy paper, I wondered how I can optimize this.

Following this stackoverflow discussion, I have now adopted a great way of optimizing TikZ pictures by placing them into separate standalone tex files.

The conference Integrable Probability Boston 2018 will be held on **May 14-18, 2018** at MIT, Cambridge, MA.

The first Integrable Probability FRG workshop was held on **October 27-29, 2017** at Columbia University in New York. Some photos from the meeting.

[2017/08/18]

We study the coarsening model (zero-temperature Ising Glauber dynamics) on $\mathbb{Z}^d$ (for $d \geq 2$) with an asymmetric tie-breaking rule. This is a Markov process on the state space ${-1,+1}^{\mathbb{Z}^d}$ of “spin configurations” in which each vertex updates its spin to agree with a majority of its neighbors at the arrival times of a Poisson process. If a vertex has equally many $+1$ and $-1$ neighbors, then it updates its spin value to $+1$ with probability $q \in [0,1]$ and to $-1$ with probability $1-q$. The initial state of this Markov chain is distributed according to a product measure with probability $p$ for a spin to be $+1$.