All entries (with papers and talks), page 2

Mont Puget at Luminy

[travel] 2017 travel plans

January

23-25 • Cleveland • Case Western Reserve University

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Yosemite waterfall in March 2016

[travel] 2016 travel

January

28 • Madison • University of Wisconsin-Madison

All travel in 2016 »

A fragment of a random heart

[event] Reading seminar on integrable probability in Spring 2017

In the Spring 2017 me and Axel Saenz will continue with the Integrable Probability Reading Seminar. This time the topic will be “From random tilings to Kardar-Parisi-Zhang universality.” In terms of content, this is not a continuation of the Fall’s seminar. In the Spring, the seminar’s aim is to give a user-friendly introduction to modern and rapidly developing topics in probability theory with connections to combinatorics, algebra, representation theory on one side, and statistical physics and many other applications on the other side.

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A flowchart for Macdonald processes and some of their specializations and limits (from talks of the authors on the subject)

5 years of Macdonald Processes

[2016/11/18]

Today marks a 5-year anniversary of the paper “Macdonald Processes” by A. Borodin and I. Corwin. It was posted on the arXiv on November 18, 2011 (arxiv.org/abs/1111.4408) and was subsequently published at Probability Theory and Related Fields (2014), Volume 158, Issue 1, pp 225–400. As of this day, Google Scholar counts 178 citations to this paper.

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Coupling of q-TASEPs and the stochastic higher spin six vertex model

[paper] Stochastic higher spin six vertex model and q-TASEPs

[2016/10/31]

We present two new connections between the inhomogeneous stochastic higher spin six vertex model in a quadrant and integrable stochastic systems from the Macdonald processes hierarchy.

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Sauron's eye

Pictures and movies of random lozenge tilings

[2016/08/20]

In Spring 2015 and Summer 2016 I used the Python and Mathematica as briefly described here to produce a number of pictures and “movies” of random lozenge tilings. Some of these pictures even appeared at an art exhibition at Harvard’s Radcliffe Institute accompanying Alexei Borodin’s fellowship.

These pictures and “movies” of random tilings are collected in this post.

Dear colleagues:

Feel free to use these pictures to illustrate your research in talks and papers, with attribution (CC BY-SA 4.0). Some of the images are available in very high resolution upon request.

Pictures and movies »

Noncolliding Bernoulli random walks

[paper] Universality of local statistics for noncolliding random walks

[2016/08/10]

We consider the $N$-particle noncolliding Bernoulli random walk — a discrete time Markov process in $\mathbb{Z}^{N}$ obtained from a collection of $N$ independent simple random walks with steps $\in{0,1}$ by conditioning that they never collide. We study the asymptotic behavior of local statistics of this process started from an arbitrary initial configuration on short times $T\ll N$ as $N\to+\infty$.

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Creation operator in a Bethe ansatz representation

[paper] Lectures on Integrable probability: Stochastic vertex models and symmetric functions

[2016/05/04]

We consider a homogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and for the q-correlation functions. At least in the case of the step initial condition, our formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six vertex model, ASEP, various q-TASEPs, and associated zero range processes.

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inhomogeneous stochastic six vertex model

[paper] Higher spin six vertex model and symmetric rational functions

[2016/01/21]

We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and for the q-correlation functions. At least in the case of the step initial condition, our formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six vertex model, ASEP, various q-TASEPs, and associated zero range processes.

Full abstract »

Moscow in December 2015

[travel] 2015 travel

January

25-29 • Paris • Inhomogeneous Random Systems conference

All travel in 2015 »