相关论文: A hyper-geometric approach to the BMV-conjecture

We construct a diffeomorphism of $\mathbb{T}^3$ admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting $T\mathbb{T}^3 = E^{cs} \oplus E^u$ and can be made…

Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and…

We show that a suitably chosen position-momentum commutator can elegantly describe many features of gravity, including the IR/UV correspondence and dimensional reduction (`holography'). Using the most simplistic example based on dimensional…

We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green…

We prove homogenization for viscous Hamilton-Jacobi equations with a Hamiltonian of the form $G(p)+V(x,\omega)$ for a wide class of stationary ergodic random media in one space dimension. The momentum part $G(p)$ of the Hamiltonian is a…

We give a combinatorial interpretation for the hypergeometric functions associated with tuples of rational numbers.

We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…

We provide a variable metric stochastic approximation theory. In doing so, we provide a convergence theory for a large class of online variable metric methods including the recently introduced online versions of the BFGS algorithm and its…

This article investigates, by probabilistic methods, various geometric questions on B_p^n, the unit ball of \ell_p^n. We propose realizations in terms of independent random variables of several distributions on B_p^n, including the…

This paper begins the exploration of what we call measures of association between two irreducible complex projective varieties of the same dimension. The idea is to study from various points of view the minimal complexity of correspondences…

A recent result about measurability of a quantum state of a single quantum system is generalized to the case of a single pre- and post-selected quantum system described by a two-state vector. The protection required for such measurement is…

Considering the simultaneous measurement of non-commuting observables, we define a geometric measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. The…

Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…

Let us consider the set of all joint probabilities generated by local binary measurements on two separated quantum systems of a given local dimension d. We address the question of whether the shape of this quantum body is convex or not. We…

We study $BV$ functions in a Hilbert space $X$ endowed with a probability measure $\nu$, assuming that $\nu$ is Fomin differentiable along suitable directions. We establish basic characterizations, and we apply the general theory to…

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…

We study atomic measures on $[0,1]$ which are invariant both under multiplication by $2\mod 1$ and by $3\mod 1$, since such measures play an important role in deciding Furstenberg's $\times 2, \times 3$ conjecture. Our specific focus was…

We characterize certain noncommutative domains in terms of noncommutative holomorphic equivalence via a pseudometric that we define in purely algebraic terms. We prove some properties of this pseudometric and provide an application to free…

We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for…

The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…