Related papers: Property tau in positive characteristic

We provide an elementary proof of the quantum adiabatic theorem.

We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension $2$.…

Random variables equidistributed on convex bodies have received quite a lot of attention in the last few years. In this paper we prove the negative association property (which generalizes the subindependence of coordinate slabs) for…

In this paper, we introduce two generalizations of the tame subgroup of the automorphism group of a polynomial ring over a domain of positive characteristic. We study detailed structures of these new `tame subgroups' in the case of two…

A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of $U$-empirical…

According to the well-known Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of $n$ independent random variables given another. In the article, we…

We obtain a version of the theorem of the square and a local structure result for actions of connected algebraic groups on seminormal varieties in characteristic 0, and arbitrary varieties in positive characteristics.

We consider asymptotics of ratios of random characteristic polynomials associated with orthogonal polynomial ensembles. Under some natural conditions on the measure in the definition of the orthogonal polynomial ensemble we establish a…

We compute the (primary) equivariant Euler characteristics of the building for the general linear group over a finite field.

Exploiting the recent work of Tao and Ziegler on a concatenation theorem on factors, we find explicit characteristic factors for multiple averages along polynomials on systems with commuting transformations, and use them to study criteria…

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…

We show that many theorems which assert that two kinds of partitions of the same integer $n$ are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics $X$ and…

A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…

Grothendieck's conjecture on p-curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all…

We consider character expansion of tau functions and multiple integrals in characters of orhtogonal and symplectic groups. In particular we consider character expansions of integrals over orthogonal and over symplectic matrices.

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 study fairness in the context of classification where the performance is measured by the area under the curve (AUC) of the receiver operating characteristic. AUC is commonly used to measure the performance of prediction models. The same…

If the prime numbers are pseudo-randomly distributed, then analogy with quantum systems suggests that counting primes might be modeled by a non-homogeneous Poisson process. Consequently, postulating underlying gamma statistics, more-or-less…

Fair division has long been an important problem in the economics literature. In this note, we consider the existence of proportionally fair allocations of indivisible goods, i.e., allocations of indivisible goods in which every agent gets…

In this paper, we first prove the variational principle for amenable packing topological pressure. Then we obtain an inequality concerning amenable packing pressure for factor maps. Finally, we show that the equality about packing…