Related papers: Height growth on semisimple groups
We study the asymptotic non-vanishing of syzygies for products of projective spaces. Generalizing the monomial methods of Ein, Erman, and Lazarsfeld \cite{einErmanLazarsfeld16} we give an explicit range in which the graded Betti numbers of…
We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly…
We apply the theory of height zeta functions to study the asymptotic distribution of rational points of bounded height on projective equivariant compactifications of semi-direct products.
Let G denote a closed, connected, self adjoint, noncompact subgroup of GL(n,R), and let d_{R} denote the canonical right invariant Riemannian metric on G. For v in R^{n} let G_{v} = {g in G : g(v) = v}. We obtain algebraically defined upper…
Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for…
In this note we consider two topics involving the relationship between the symplectic capacity and the mean width of convex bodies in $\mathbb{R}^{2n}$. We first describe an alternative path from the symplectic Brunn-Minkowski inequality of…
Let $G$ be an anisotropic semisimple group over a totally real number field $F$. Suppose that $G$ is compact at all but one infinite place $v_0$. In addition, suppose that $G_{v_0}$ is $\mathbb{R}$-almost simple, not split, and has a Cartan…
In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main…
We consider the Hardy-Littlewood maximal function associated with ball averages on spaces with exponential volume growth. We focus on discrete groups with balls defined by invariant metrics associated with a variety of length functions.…
This paper proves that in a non-elementary relatively hyperbolic group, the logarithm growth rate of any non-elementary subgroup has a linear lower bound by the logarithm of the size of the corresponding generating set. As a consequence,…
We explain how to deduce from the multi-height analysis of rational points on a toric stack (respectively on a toric variety) the asymptotic study of the number of rational points of bounded orbifold anticanonical height (respectively…
The density of a subgroupoid with respect to a free groupoid is defined as the asymptotic ratio of their growths. This notion can be interpreted as a generalisation of the index's inverse for groups or as the probability of an element…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
In this paper we study the systole growth of arithmetic locally symmetric spaces up congruence covers and show that this growth is at least logarithmic in volume. This generalizes previous work of Buser and Sarnak as well as Katz, Schaps…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
We introduce and study the notion of \emph{semiadditive height} for higher semiadditive $\infty$-categories, which generalizes the chromatic height. We show that the higher semiadditive structure trivializes above the height and prove a…
We use circle method prove an asymptotic local-global theorem on the heights of point orbits of thin subgroups of Bianchi groups in $\mathbb H^3$.
Markovian growth-fragmentation processes introduced by Bertoin extend the pure fragmentation model by allowing the fragments to grow larger or smaller between dislocation events. What becomes of the known asymptotic behaviors of…
Since laws of physics exist in nature, their possible relationship to terrestial growth is introduced. By considering the human body as a dynamic system of variable mass (and volume), growing under a gravity field, it is shown how natural…
Asymptotic quadratic growth rates of saddle connections and families of periodic cylinders on translation tori with n marked points are studied. For any marking the existence of limits of the quadratic growth rate is shown using elementary…