arXiv research

New knots show infinite spectrum of tunnel number growth rate.

World GDP growth is predicted to become unsustainable.

Calculates the growth rate of m-small knots' tunnel numbers.

Classifies polynomial growth solutions to drift-harmonic equations on asymptotically paraboloidal manifolds.

Study on MLE growth rate for stable CIR process, proving consistency and normality.

Study maximum likelihood estimator for growth rate of jump-type CIR process.

Growth rate of Dehn twist lattice points in Teichmüller space is slower than mapping class group lattice points.

New growth rate for pseudo-Anosov conjugacy classes in Teichmüller space.

Uniqueness of asymptotic limits for Ricci-flat manifolds with linear volume growth is proven.

This paper analyzes deep Stable neural networks, showing convergence rates under different growth settings.

Universal portfolio strategy aims for best growth rate in stochastic markets.

Early warning signs of Greece's economic crisis were present in GDP growth rate instability.

In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature (cmc) 1 in $\R^{n}$ (Delaunay unduloids). When $n=3$, using the asymptotics result of Korevaar, Kusner and Solomon, we derive an explicit asymptotic index growth rate for finite topology cmc 1 surfac…

Paper introduces new risk measures for Kelly criterion.

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…

The main theme of this paper is to study for a symplectomorphism of a compact surface, the asymptotic invariant which is defined to be the growth rate of the sequence of the total dimensions of symplectic Floer homologies of the iterates of the symplectomorphism. We prove that the asymptotic invariant coincides with as…

For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $λ\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading s…

Study proves uniqueness of asymptotic limits for specific manifolds.

Study counts geodesics on special projective planes, finding a noninteger growth rate.

Let X be a Hadamard manifold and $Γ$ a discrete group of isometries of X which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the geometric limit set of $Γ$ in order to derive a new asymptotic estimate for the growth rate of closed geodesics in not necessar…

Study optimizes growth rate for investors with long-only constraints.

Given a knot $K$ in a closed orientable manifold $M$ we define the growth rate of the tunnel number of $K$ to be $gr_t(K) = \limsup_{n \to \infty} \frac{t(nK) - n t(K)}{n-1}$. As our main result we prove that the Heegaard genus of $M$ is strictly less than the Heegaard genus of the knot exterior if and only if the grow…

The study calculates the growth rate of reciprocal hyperbolic elements in Hecke groups.

A strategy ensures maximal wealth growth in competitive asset markets.

The paper optimizes wealth growth in uncertain models of asset markets.

Study on harmonic functions in spaces with collapsing behaviors.

We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent $ζ=3$. Because of data limitations, previous studies in this field have b…

Investigates optimal portfolio strategies in markets with latent side information.

Optimal portfolio strategy found as fixed costs approach zero.

We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal growth rate, which can be …

Study on the growth of colored Jones polynomial for figure-eight knot cables.

Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when th…

Study shows exponential growth of knot polynomial tied to Chern-Simons invariant.

Study shows how margin loan interest rates converge to a choke price, limiting long-term advantage in the broker call money market.

Random surfaces' diameter grows logarithmically with size.

Study high-frequency trading with fractional Brownian motion, finding optimal strategies and convergence.

Study on $k$-surfaces in negatively curved 3-manifolds, focusing on energy and entropy.

The study examines the growth of reciprocal classes in Hecke groups, proving an asymptotic formula.

Study excursions of geodesics in RAAGs and graph products, finding a log(n) max excursion.

Graph complexity and Mahler measure linked through spanning trees.

The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{po…

Develops a new model-free approach to portfolio theory using rough paths.

We present a preferential attachment growth model to obtain the distribution $P(K)$ of number of units $K$ in the classes which may represent business firms or other socio-economic entities. We found that $P(K)$ is described in its central part by a power law with an exponent $φ=2+b/(1-b)$ which depends on the probabil…

Study on multiplicities in length spectrum of Salem numbers.

In this paper we develop an asymptotic analysis for formal and actual solutions of q-difference equations, under a regularity assumption. In particular, evaluations of regular solutions of regular q-difference equations have an exponential growth rate which can be computed from the q-difference equation. The motivation…

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent 3. Because of data limitations, previous studies in this field hav…

We consider the asymptotics of the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic $3$-manifold, evaluated at the root of unity $\exp({2π\sqrt{-1}}/{r})$ instead of the standard $\exp({π\sqrt{-1}}/{r})$. We present evidence that, as $r$ tends to $\infty$, these invariants grow exponentially with growt…

Game theory model shows optimal investment strategy for wealth growth.