Observables of stochastic colored vertex models and local relation

Hidden diagonal integrability of $q$-Hahn vertex model and Beta polymer model

We study a new integrable probabilistic system, defined in terms of a stochastic colored vertex model on a square lattice. The main distinctive feature of our model is a new family of parameters attached to diagonals rather than to rows or columns, like in other similar models. Because of these new parameters the previously known results about vertex models cannot be directly applied, but nevertheless the integrability remains, and we prove explicit integral expressions for $q$-deformed moments of the (colored) height functions of the model. Following known techniques our model can be interpre…

环上彩色相互作用粒子系统：来自Yang-Baxter方程的平稳测度

Colored Interacting Particle Systems on the Ring: Stationary Measures from Yang-Baxter Equation

本文基于Yang-Baxter方程和可积随机顶点模型，提出统一方法构造环和直线上多物种粒子系统（mASEP、q-Boson、q-PushTASEP）的平稳测度，并证明彩色Burke定理及计算平稳粒子流。

Observables of coloured stochastic vertex models and their polymer limits

In the context of the coloured stochastic vertex model in a quadrant, we identify a family of observables whose averages are given by explicit contour integrals. The observables are certain linear combinations of $q$-moments of the coloured height functions of the model. In a polymer limit, this yields integral representations for moments of partition functions of strict-weak, semi-discrete Brownian, and continuum Brownian polymers with varying beginning and ending points of the polymers.

Indistinguishable sceneries on the Boolean hypercube

We show that the scenery reconstruction problem on the Boolean hypercube is in general impossible. This is done by using locally biased functions, in which every vertex has a constant fraction of neighbors colored by $1$, and locally stable functions, in which every vertex has a constant fraction of neighbors colored by its own color. Our methods are constructive, and also give super-polynomial lower bounds on the number of locally biased and locally stable functions. We further show similar results for $\mathbb{Z}^n$ and other graphs, and offer several follow-up questions.