Related papers: Lectures on Integrable probability: Stochastic ver…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we…
Many integrable stochastic particle systems in one space dimension (such as TASEP - Totally Asymmetric Simple Exclusion Process - and its $q$-deformation, the $q$-TASEP) remain integrable if we equip each particle with its own speed…
We derive an integral expression for the leading-order type I-I-I three-point functions in the $\mathfrak{su}(2) $-sector of $\mathcal{N}=4$ super Yang-Mills theory, for which no determinant formula is known. To this end, we first map the…
Fully packed loop models describe the statistics of closely packed nested polygons on the square lattice. Many exact results can be obtained for these models, even for finite geometries, using their close relationship to alternating-sign…
The notion of periodic two-scale convergence and the method of periodic unfolding are prominent and useful tools in multiscale modeling and analysis of PDEs with rapidly oscillating periodic coefficients. In this paper we are interested in…
In this article, we consider a class of functions on $\mathbb{R}^d$, called positive homogeneous functions, which interact well with certain continuous one-parameter groups of (generally anisotropic) dilations. Generalizing the Euclidean…
We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but…
Stable spin Hall-Littlewood symmetric polynomials labeled by partitions were recently introduced by Borodin and Wheeler in the context of higher spin six vertex models, which are one-parameter deformation of the Hall-Littlewood polynomials.…
We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer…
We investigate the elliptic integrable model introduced by Deguchi and Martin, which is an elliptic extension of the Perk-Schultz model. We introduce and study a class of partition functions of the elliptic model by using the…
The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of two- and three-state vertex models. These models include the…
This work studies the tail exponents for the height function of the stationary stochastic six vertex model in the moderate deviations regime. For the upper tail of the height function we find upper and lower bounds of matching order, with a…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
Starting from the motional property of functional field based on the action principle of path integral formulation while proposing maximum coherence motion principle and maximum locally entangled-qubits motion principle as guiding…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colourings or the number of independent sets of a graph and also the partition…
We have found a family of solvable nineteen vertex model with statistical configurations invariant by the time reversal symmetry within a systematic study of the respective Yang-Baxter relation. The Boltzmann weights sit on a degree seven…
This paper investigates quasi-homogeneous integrable systems by analyzing their Laurent series solutions near movable singularities, motivated by patterns observed in Kovalevskaya exponents of four-dimensional Painlev\'e-type equations. We…
This work deals with the homogenization of functionals with linear growth in the context of $\mathcal{A}$-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the…