### A sign in Boston Logan airport commemorating deformed Bosons

This sign works equally well for both $q$-Bosons and $t$-Bosons, so the choice of parameter is up to the tourist.

#### References

1. T. Sasamoto and M. Wadati, Exact results for one-dimensional totally asymmetric diffusion models, J. Phys. A 31 (1998), 6057–6071

2. 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]

[2017/12/21]

### (An update on the previous post)

So, I had a problem - my TeX distribution is new and updated, but I need to submit a paper to the arXiv, and arXiv has a different version of TeX distribution (currently 2016). The main problem is biblatex, which creates an incompatible version of the bibliography .bbl file. For this, I need an appropriate version of the biblatex package.

### 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.

### 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 $U_q(\widehat{\mathfrak{sl}_2})$. 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.

### Gallery of simulations of integrable stochastic systems

Updated gallery of simulations of integrable stochastic systems

### 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.

### External Tikz pictures

[2017/12/12]

I produce almost all pictures in my math $\mathrm{\LaTeX}$ 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.