Related papers: Lectures on Integrable probability: Stochastic ver…
Let U be a homogeneous variety over Q of a linear algebraic group. Choose an integral model and assume the existence of infinitely many integral points. Then one would like to give an asymptotic count of integral points of bounded height…
We give a summary of the results from Parts I-V (math.RT/9804086, math.RT/9804087, math.RT/9804088, math.RT/9810013, math.RT/9810014). Our work originated from harmonic analysis on the infinite symmetric group. The problem of spectral…
We study an inhomogenous multispecies version of the Totally Asymmetric Simple Exclusion Process (TASEP) on a periodic oriented one dimensional lattice, which depends on two sets of parameters $({\bf \tau},{\bf \nu})$, attached to the…
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
Representation learning is a fundamental task in machine learning, aiming at uncovering structures from data to facilitate subsequent tasks. However, what is a good representation for planning and reasoning in a stochastic world remains an…
We examine the wavefunctions and their scalar products of a one-parameter family of integrable five vertex models. At a special point of the parameter, the model investigated is related to an irreversible interacting stochastic particle…
We consider the group $\mathrm{Aut}(T)$ of isometries of a semi-homogeneous tree $T=T_{q_+,q_-}$ with valencies $q_+ +1$ and $q_- +1$ and its two orbits $V_+$, $V_-$ respectively. We make use of the action of $\mathrm{Aut} (T)$ to equip the…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
In this work, we introduce a theory of stochastic integration with respect to symmetric $\alpha$-stable cylindrical L\'evy processes. Since $\alpha$-stable cylindrical L\'evy processes do not enjoy a semi-martingale decomposition, our…
In this work, we describe a generic approach to show convergence with high probability for stochastic convex optimization. In previous works, either the convergence is only in expectation or the bound depends on the diameter of the domain.…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…
We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following…
Machine learning typically presupposes classical probability theory which implies that aggregation is built upon expectation. There are now multiple reasons to motivate looking at richer alternatives to classical probability theory as a…
In this work, we study multiplicity-free induced representations of finite groups. We analyze in great detail the structure of the Hecke algebra corresponding to the commutant of an induced representation and then specialize to the…
We use spin-coherent states as a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of…
We show that the celebrated six-vertex model of statistical mechanics (along with its multistate generalizations) can be reformulated as an Ising-type model with only a two-spin interaction. Such a reformulation unravels remarkable…
In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a certain limit regime recently predicted by Borodin-Corwin-Gorin. This convergence holds for…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
We generalize the Hopf algebras of free quasisymmetric functions, quasisymmetric functions, noncommutative symmetric functions, and symmetric functions to certain representations of the category of all finite Coxeter systems and its dual…
An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…