[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 $+1$.

15-28 • Creswick (Victoria, Australia) • “Non-equilibrium systems and special functions” program at MATRIX Institute

A three-week program which brought together numerous leading experts in random matrices and related fields. For me personally this program has started a very exciting collaboration on probabilistic understanding of combinatorial summation identities.

[2017/06/04]

I came across a very nice
source file beautifier called `latexindent`

which is a part
of the standard
distribution.

The script should be run on the source and it would do the stuff I usually like in source files, such as wrapping, indentation of lists and environments, and so on.

The issue with
source files is that everyone using
formats them differently, since the
processing is very forgiving.
In particular, there is lots of whitespace which can be inserted to make
source files more human readable.
The `latexindent`

tool would allow me to *automatically* standardize
the source code and not think about the various ways one can format the
source.

(Previously in some projects,
in particular in joint ones,
I have spent some time reformatting the source files
to my liking; and while `latexindent`

might not format everything
how I would like, it is extremely configurable, and I can live with it
because of the time it would save me.)

[2017/05/20]

I’ve updated and streamlined the internal structure of my homepage which will make it much easier to manage. This is yet another attempt to better understand Jekyll and come up with a website which is easy to manage and update regularly.

In the process of the update I’ve moved over almost all content from the previous version (also build with Jekyll, but back in January 2014), and in particular created a special gallery of simulations instead of a series of posts like in the previous version (although these simulations are also displayed in posts).

The design of the homepage closely follows the style of University of Virginia, and is in line with the new Math Department website which I am also building.

From the conference website:

This special edition of the Southeast Probability Conference will focus on interacting particle systems, random graphs, stochastic growth models, and their applications in biology, ecology, and statistical physics. It is also an occasion to honor the contributions of Professor Rick Durrett on the occasion of his 65th birthday.

From the workshop website:

Universality of Kardar-Parisi-Zhang (KPZ) scalings is one the most active areas in statistical mechanics and mathematical physics in the last 10 years.

[2017/03/22]

We study asymptotics of $q$-distributed random lozenge tilings of sawtooth domains (equivalently, of random interlacing integer arrays with fixed top row). Under the distribution we consider each tiling is weighted proportionally to $q^{\mathsf{vol}}$, where $\mathsf{vol}$ is the volume under the corresponding 3D stepped surface.

[2017/03/10]

We introduce and study the inhomogeneous exponential jump model — an integrable stochastic interacting particle system on the continuous half line evolving in continuous time. An important feature of the system is the presence of arbitrary spatial inhomogeneity on the half line which does not break the integrability. We completely characterize the macroscopic limit shape and asymptotic fluctuations of the height function (= integrated current) in the model.

The Seminar on Stochastic Processes (SSP) in 2017 is held from **Wednesday, March 8, through Saturday, March 11**. It is hosted by the University of Virginia. Conference website.