A multilayer pushTASEP simulation

Simulations of inhomogeneous multilayer pushTASEP

[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.

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Forward transition probabilities associated with the Yang-Baxter field

Yang-Baxter field for spin Hall-Littlewood symmetric functions

[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.

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arXiv logo

Switching TeXLive distributions for arXiv

[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.

How to switch TeXLive versions »

External Tikz pictures

[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.

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Uniformly random tiling of a hexagon with a hole

Integrable Probability Boston 2018

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

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FRG meeting in October 2017

First FRG workshop, October 2017, Columbia University

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

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This is how the GUE Tracy-Widom/Airy$_2$ double critical point is deformed in the

Coarsening model on with biased zero-energy flips and an exponential large deviation bound for ASEP

[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 $+1$.

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