Related papers: Hensel minimality, $p$-adic exponentiation and Tat…

We introduce $p$-uniformity to characterize the scaling of density fluctuations in spatial random systems in $\mathbb{R}^d$, ranging from hyperfluctuation to stealthy hyperuniformity. Our central theorem establishes sufficient conditions to…

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

Let F be a non-archimedean local field of odd residual characteristic p. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu's construction of complex…

We establish uniform bounds on the multiplicities of irreducible admissible representations appearing in spaces of functions on symmetric spaces over $p$-adic fields. These multiplicities can exceed one and depend intricately on the group,…

We introduce on any smooth oriented minimal surface in Euclidean $3$-space a meromorphic quadratic differential, $P$, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of…

In the previous article (S. Matsutani and Y. Shimosako and Y. Wang, Physica A \bf{391} (2012) 5802-5809) we numerically investigated an electric potential problem with high contrast local conductivities ($\gamma_0$ and $\gamma_1$,…

Using the Tannakian formalism, we formulate conjectural analogs of Chebotar\"ev's Density Theorem for $F$-isocrystals over a smooth geometrically irreducible variety defined over a finite field. We prove these analogs for several large…

We study combinatorial structures arising from finite-time transition probabilities of the Totally Asymmetric Simple Exclusion Process with open boundary conditions. While much of the existing combinatorial theory regarding the TASEP…

This thesis addresses the theory of topological spaces and the foundations of persistence theory. We will discuss chain complexes and the associated simplicial homology groups, as well as their relationship with singular homology theory.…

We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the real line is asymptotically equivalent to this density times…

Let $T$ be a complete, model complete o-minimal theory extending the theory of real closed ordered fields and assume that $T$ is power bounded. Let $K$ be a model of $T$ equipped with a $T$-convex valuation ring $\mathcal{O}$ and a…

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…

From the generalized Riemann hypothesis for motivic L-functions, we derive an effective version of the Sato-Tate conjecture for an abelian variety A defined over a number field k with connected Sato-Tate group. By effective we mean that we…

We present a version of Smale's $\alpha$-theory for ultrametric fields, such as the $p$-adics and their extensions, which gives us a multivariate version of Hensel's lemma.

For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced…

We provide polynomial upper bounds for the minimal sizes of distal cell decompositions in several kinds of distal structures, particularly weakly $o$-minimal and $P$-minimal structures. The bound in general weakly $o$-minimal structures…

Given two maps between smooth manifolds, the obstruction to removing their coincidences (via homotopies) is measured by minimum numbers. In order to determine them we introduce and study an infinite hierarchy of Nielsen numbers N_i, i = 0,…

The concept of differential uniformity was recently extended to the $c$-differential uniformity. An interesting problem in this area is the construction of functions with low $c$-differential uniformity and a lot of research has been done…

We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly solvable examples of tandem queues, directed…

This paper provides a full characterization for when the expansion of a complete o-minimal theory by a unary predicate that picks out a divisible dense and codense subgroup has a model companion. This result is motivated by criteria and…