arXiv research

Study finds minimum growth rate for surface solutions.

Proves minimal growth rate for Coxeter groups in hyperbolic space.

New groups found in hyperbolic 4D and 5D space have minimal growth rate.

Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.

Enhanced Gordon growth model for valuing financial products.

Optimal Liouville theorem for minimal disks in any codimension.

We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region $E$ and instantaneous covariation $c$ are known, and where additionally the assets are stable in that their occupancy time measures converg…

Minimal submanifolds confined in space are highly restricted.

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as l…

Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a constant depending only, and necessarily, on S. For the proof, we find in any suc…

The paper calculates the growth rates of billiard languages in hyperbolic polygons.

Growth rates of geodesics on modular orbifolds are studied.

Game theory model shows optimal investment strategy for wealth growth.

Study finds many nonplanar minimal spheres in elongated ellipsoids.

Study growth rates of subgroups in groups with a constricting element.

New proof shows not all Salem numbers are growth rates of Coxeter groups.

This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.

We define a large class of abstract Coxeter groups, that we call $\infty$--spanned, and for which the word growth rate and the geodesic growth rate appear to be Perron numbers. This class contains a fair amount of Coxeter groups acting on hyperbolic spaces, thus corroborating a conjecture by Kellerhals and Perren. We a…

Study confined subgroups in groups with contracting elements, showing their growth rate is strictly greater than half of the ambient growth rate.

Growth rate of the world Growth Domestic Product (GDP) is analysed to determine possible pathways of the future economic growth. The analysis is based on using the latest data of the World Bank and it reveals that the growth rate between 1960 and 2014 was following a trajectory approaching asymptotically a constant val…

The paper explores growth rates and Perron numbers in Coxeter systems with low-dimensional Davis complexes.

Cooperation is a persistent behavioral pattern of entities pooling and sharing resources. Its ubiquity in nature poses a conundrum. Whenever two entities cooperate, one must willingly relinquish something of value to the other. Why is this apparent altruism favored in evolution? Classical solutions assume a net fitness…

Study bounds growth rate of irreducible meanders, showing proportion vanishes.

Mathematical study of excess growth rate connects info theory with finance.

In this paper, asymptotic results in a long-term growth rate portfolio optimization model under both fixed and proportional transaction costs are obtained. More precisely, the convergence of the model when the fixed costs tend to zero is investigated. A suitable limit model with purely proportional costs is introduced …

This paper investigates the statistical properties of within-country GDP and industrial production (IP) growth rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether als…

We present a quantitative characterisation of the fluctuations of the annualized growth rate of the real US GDP per capita growth at many scales, using a wavelet transform analysis of two data sets, quarterly data from 1947 to 2015 and annual data from 1800 to 2010. Our main finding is that the distribution of GDP grow…

Proof shows cones minimize certain geometric functionals.

Bubbles are essential in certain economic models with high growth and low interest rates.

Direct proof shows adaptive gradient descent converges near-linearly for convex functions.

Study on Monge-Ampère equations with polynomial growth rates.

Investigates the relationship between US money supply and asset indices over 2001-2019.

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety…

Optimizes portfolio growth rate for a behavioral investor considering terminal relative growth rate.

Study counts minimal Lagrangians in hyperbolic surfaces with precise growth rate.

Minimal graphs over simply connected domains grow at most exponentially.

In [6], Kellerhals and Perren conjectured that the growth rates of the reflection groups given by hyperbolic Coxeter polyhedra are always Perron numbers. We prove that this conjecture is always true for the case of ideal Coxeter polyhedra in $\mathbb{H}^3$. We also find out the ideal Coxeter polyhedron in $\mathbb{H}^3…

The study examines how automorphism growth rates of a group can be deduced from its simpler decompositions.

In a previous paper the authors defined the growth rate of the tunnel number of knots, an invariant that measures that asymptotic behavior of the tunnel number under connected sum. In this paper we calculate the growth rate of the tunnel number of m-small knots in terms of their bridge indices.

In a previous paper Kobayashi and Rieck defined the growth rate of the tunnel number of a knot $K$, a knot invariant that measures the asymptotic behavior of the tunnel number under iterated connected sum of $K$. We denote the growth rate by $\mbox{gr}_t(K)$. In this paper we construct, for any $ε> 0$, a hyperbolic kno…

Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all firm levels, yields Zipf's law under a balance condition between the effective grow…

Warning signs about the developing economic crisis in Greece were present in the growth rate of the Gross Domestic Product (GDP) and in the growth of the GDP well before the economic collapse. The growth rate was strongly unstable. On average, in less than 50 years, it decreased 10-folds but after reaching a low minimu…

We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups. A detailed study of the uniform exponential growth rate of closed 3-manifold groups is also presented.

Upper bounds for essential spectrum of minimal submanifolds linked to volume growth.

We study arithmetic properties of the growth rates of cofinite 3-dimensional hyperbolic Coxeter groups whose dihedral angles are of the form $\fracπ{m}$ for $m=2,3,4,5,6$ and show that the growth rates are always Perron numbers.

The paper discusses the role of monetary policy when potential output depends on the inflation rate. If the intention of the central bank is to maximize actual output growth, then it has to be credibly committed to a strict inflation targeting rule, and to take the MOGIR (the Maximizing Output Growth Inflation Rate) as…

In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra some of its dihedral angles are $\fracπ{m}$ for $m\geq{7}$. By combining with the classical result by Parry \cite{Pa} and the main result of \cite{Y}, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Pe…

Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…