Related papers: An Elementary Approach to Free Entropy Theory for …

Let $(X_1,\dots,X_m)$ be self-adjoint non-commutative random variables distributed according to the free Gibbs law given by a sufficiently regular convex and semi-concave potential $V$, and let $(S_1,\dots,S_m)$ be a free semicircular…

Talagrand's inequalities make a link between two fundamentals concepts of probability: transport of measures and entropy. The study of the counterpart of these inequalities in the context of free probability has been initiated by Biane and…

In arXiv:1304.0630, it was shown that convex, almost everywhere continuous functions coordinatize a broad class of probability measures on $\mathbb{R}^n$ by the map $U \mapsto (\nabla U)_{\#} e^{-U} dx$. We consider whether there is a…

One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ variables has a spectral distribution that converges…

We construct non-commutative analogs of transport maps among free Gibbs state satisfying a certain convexity condition. Unlike previous constructions, our approach is non-perturbative in nature and thus can be used to construct transport…

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…

Given $\epsilon \in (0,1)$, a probability measure $\mu$ on $\Omega\subset\mathbb{R}^p$ and a semi-algebraic set $K\subset X\times\Omega$, we consider the feasible set $X^*_\epsilon=\{x\in X:{\rm Prob}[(x,\omega)\in K]\geq 1-\epsilon\}$…

In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized elliptic PDEs with finite-dimensional deterministic and…

Suppose we are given the free product V of a finite family of finite or countable sets. We consider a transient random walk on the free product arising naturally from a convex combination of random walks on the free factors. We prove the…

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…

We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…

We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…

In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…

In many channel measurement applications, one needs to estimate some characteristics of the channels based on a limited set of measurements. This is mainly due to the highly time varying characteristics of the channel. In this contribution,…

We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent…

We study solutions to the free stochastic differential equation $dX_t = dS_t - \half DV(X_t)dt$, where $V$ is a locally convex polynomial potential in $m$ non-commuting variables. We show that for self-adjoint $V$, the law $\mu_V$ of a…

Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…

We study asymptotic expansions in free probability. In a class of classical limit theorems Edgeworth expansion can be obtained via a general approach using sequences of "influence" functions of individual random elements described by…

In this paper we introduce a notion of free energy and large deviations rate function for asymptotically additive sequences of potentials via an approximation method by families of continuous potentials. We provide estimates for the…

The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…