Related papers: Effective equidistribution and property tau

We consider the problem of fair division, where a set of indivisible goods should be distributed fairly among a set of agents with combinatorial valuations. To capture fairness, we adopt the notion of shares, where each agent is entitled to…

Heyde proved that a Gaussian distribution on a real line is characterized by the symmetry of the conditional distribution of one linear form given another. The present article is devoted to an analog of the Heyde theorem in the case when…

In this paper, we prove the equidistribution of saddle periodic points for Henon-type automorphisms of C^k with respect to it equilibrium measure. A general strategy to obtain equidistribution properties in any dimension is presented. It is…

We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…

We show that a Kirkwood-Dirac type quasiprobability distribution is sufficient to reveal any arbitrary quantum resource. This is achieved by demonstrating that it is always possible to identify a set of incompatible measurements that…

Based on entropy and symmetrical uncertainty (SU), we define a metric for categorical random variables and show that this metric can be promoted into an appropriate quotient space of categorical random variables. Moreover, we also show that…

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis that the actions have finite geometric…

We consider a class of homogeneous manifolds over a simple Lie group which appears in the problem of classification of homogeneous manifolds with reductive subgroups of maximal rank as stabilizer of a point. We prove that any manifold of…

In this paper, we obtain a quantitative estimate of unique continuation and an observability inequality from an equidistributed set for solutions of the diffusion equation in the whole space RN. This kind of observability indicates that the…

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple…

We highlight the tension between stability and equality in non transferable utility matching. We consider many to one matchings and refer to the two sides of the market as students and schools. The latter have aligned preferences, which in…

We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…

We consider the problem of allocating indivisible goods in a way that is fair, using one of the leading market mechanisms in economics: the competitive equilibrium from equal incomes. Focusing on two major classes of valuations, namely…

We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation…

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems…

We study a variant of the equidistribution of mass conjecture on the sphere posed by B\"ocherer, Sarnak, and Schulze-Pillot: quantum unique ergodicity in shrinking sets. Conditionally on the generalized Lindel\"of hypothesis, we show that…

We study fair division of indivisible goods in a single-parameter environment. In particular, we develop truthful social welfare maximizing mechanisms for fairly allocating indivisible goods. Our fairness guarantees are in terms of solution…

In the unit tangent bundle of noncompact finite volume negatively curved Riemannian manifolds, we prove the equidistribution towards the measure of maximal entropy for the geodesic flow of the Lebesgue measure along the divergent geodesic…

We generalize an equidistribution theorem \`a la Bader-Muchnik for operator-valued measures constructed from a family of boundary representations associated with Gibbs measures in the context of convex cocompact discrete group of isometries…

We develop a framework of parametrized semiadditivity and stability with respect to so-called atomic orbital subcategories of an indexing $\infty$-category $T$, extending work of Nardin. Specializing this framework, we introduce global…