We report universal statistical properties displayed by ensembles of pure states that
naturally emerge in quantum many-body systems. Specifically, two classes of state …

The field of property testing originated in work on program checking, and has evolved into
an established and very active research area. In this work, we survey the developments of …

We propose a general methodology for the construction and analysis of essentially minimax
estimators for a wide class of functionals of finite dimensional parameters, and elaborate on …

Consider the problem of estimating the Shannon entropy of a distribution over elements from
independent samples. We show that the minimax mean-square error is within the universal …

We consider the problem of verifying the identity of a distribution: Given the description of a
distribution over a discrete finite or countably infinite support, p=(p_1,p_2,...), how many …

We study the question of closeness testing for two discrete distributions. More precisely,
given samples from two distributions p and q over an n-element set, we wish to distinguish …

Estimation of Wasserstein distances in the Spiked Transport Model Page 1 Bernoulli 28(4),
2022, 2663–2688 https://doi.org/10.3150/21-BEJ1433 Estimation of Wasserstein distances …

We show that a class of statistical properties of distributions, which includes such practically
relevant properties as entropy, the number of distinct elements, and distance metrics …

Here we study the comparative power of classical and quantum learners for generative
modelling within the Probably Approximately Correct (PAC) framework. More specifically we …

We consider the problem of estimating the support size of a discrete distribution whose
minimum nonzero mass is at least 1 k. Under the independent sampling model, we show …