相关论文: Projections of Orbital Measures and Quantum Margin…

We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen's theorem for correlated probability,…

We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…

Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on…

The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…

We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…

We consider random stochastic matrices $M$ with elements given by $M_{ij}=|U_{ij}|^2$, with $U$ being uniformly distributed on one of the classical compact Lie groups or associated symmetric spaces. We observe numerically that, for large…

This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections…

We investigate algebraicity properties of quotients of complex spaces by complex reductive Lie groups G. We obtain a projectivity result for compact momentum map quotients of algebraic G-varieties. Furthermore, we prove equivariant versions…

We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…

We prove the expected disturbance caused to a quantum system by a sequence of randomly ordered two-outcome projective measurements is upper bounded by the square root of the probability that at least one measurement in the sequence accepts.…

We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of…

We give a proof of the Universality Conjecture for orthogonal and symplectic ensembles of random matrices in the scaling limit for a class of weights w(x)=exp(-V(x)) where V is a polynomial, V(x)=kappa_{2m}x^{2m}+..., kappa_{2m}>0. For such…

Projection factors describe the contraction of Lebesgue measures in orthogonal projections between subspaces of a real or complex inner product space. They are connected to Grassmann's exterior algebra and the Grassmann angle between…

Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations…

In this paper we make a review of the results obtained in previous works by the authors on deformation quantization of coadjoint orbits of semisimple Lie groups. We motivate the problem with a new point of view of the well known Moyal-Weyl…

We compute the asymptotic behavior of the average-case filling volume for certain models of random Lipschitz cycles in the unit cube and sphere. For example, we estimate the minimal area of a Seifert surface for a model of random knots…

This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent…

Wigner's marginal probability theory is revisited, and systematically applied to n-particle correlation measurements. A set of Bell inequalities whose corollaries are Hardy contradiction and its generalisation are derived with intuitive…

Non-commutative spacetime and quantum groups have been argued to capture non-classical features of spacetime and its symmetries in the low-energy limit of quantum gravity. In this letter, we show that employing the $SU_q(2)$ quantum group…

We attempt to reconstruct the irreducible unitary representations of the Banach Lie group $U_0(\H)$ of all unitary operators $U$ on a separable Hilbert space $\H$ for which $U-{\mathbb I}$ is compact, originally found by Kirillov and…