Related papers: Hidden Symmetries of Stochastic Models
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
The exact stationary state of an asymmetric exclusion process with fully parallel dynamics is obtained using the matrix product Ansatz. We give a simple derivation for the deterministic case by a physical interpretation of the dimension of…
Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials. Then the Dunkl-Cherednik operator of which they are eigenfunctions, is…
Symmetries play a conspicuous role in the large-scale behavior of critical systems. While in equilibrium they allow to classify asymptotics into different universality classes, out of equilibrium they can emerge, some times unexpectedly, as…
We define a special matrix multiplication among a special subset of $2N\x 2N$ matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative…
Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state…
We introduce a multi-species generalization of the asymmetric simple exclusion process (ASEP) with a ``no-passing" constraint, forbidding overtaking, on a one-dimensional open chain. This no-passing rule fragments the Hilbert space into an…
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
Statistical mechanics and thermodynamics for ideal fractional exclusion statistics with mutual statistical interactions is studied systematically. We discuss properties of the single-state partition functions and derive the general form of…
As was shown in \cite{GPS} the matrix $L=|| l_i^j||$ whose entries $l_i^j$ are generators of the so-called reflection equation algebra is subject to some polynomial identity looking like the Cayley-Hamilton identity for a numerical matrix.…
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete…
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…
Small representations of a group bring us to large symmetries in a representation space. Analysis on minimal representations utilises large symmetries in their geometric models, and serves as a driving force in creating new interesting…
We study the quantum fermionic billiard defined by the dynamics of a quantized supersymmetric squashed three-sphere (Bianchi IX cosmological model within D=4 simple supergravity). The quantization of the homogeneous gravitino field leads to…
In this paper we analyze the steady state of the Asymmetric Simple Exclusion process with open boundaries and second class particles by deforming it through the introduction of spectral parameters. The (unnormalized) probabilities of the…
We show that the series product, which serves as an algebraic rule for connecting state-based input/output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum…