Related papers: Error Estimates in Horocycle Averages Asymptotics:…
We prove that the orbit of a non-periodic point at prime values of the horocycle flow in the modular surface is dense in a set of positive measure. For some special orbits we also prove that they are dense in the whole space (assuming the…
Strongly consistent estimates are shown, via relative frequency, for the probability of "white balls" inside a dichotomous urn when such a probability is an arbitrary continuous time dependent function over a bounded time interval. The…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…
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…
Collective cell migration lies at the intersection of developmental biology and non-equilibrium physics, where active processes give rise to emergent patterns that are biologically relevant. Here, we investigate dilatational modes--cycles…
We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis formulated in terms of integrals of the…
We study whether the universal runaway behaviour of stringy scalar potentials towards infinite field distance limits can produce an accelerated expanding cosmology \`{a} la quintessence. We identify a loophole to some proposed bounds that…
The logarithmic asymptotics for the growth of the number of periodic orbits, such that the norm of the corresponding renormalization matrix does not exceed a given constant, is computed for the Teichmueller flow on Veech's moduli space of…
We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with…
In this paper we give an asymptotic expansion including error terms for the number of cycles in homology classes for connected graphs. Mainly, we obtain formulae about the coefficients of error terms which depend on the homology classes and…
We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…
For uniform random permutations conditioned to have no long cycles, we prove that the total number of cycles satisfies a central limit theorem. Under additional assumptions on the asymptotic behavior of the set of allowed cycle lengths, we…
We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\lambda,a,s)=\sum_{n=1}^\infty \exp (2\pi ni\lambda)/(n+a)^s$ for large complex values of $a$, with $\lambda$ and $s$ regarded as parameters. It is…
We carefully examine the Polyakov path integral for strings on $\text{AdS}_3$ in superspace, both for type II and heterotic superstrings. We construct a free-field realization of the supersymmetric $\text{SL}(2,\mathbb{R})$ WZW model which…
The aim of this paper is to offer an analytic theory of the shear banding instability in amorphous solids that are subjected to athermal quasi-static shear. To this aim we derive nonlinear equations for the displacement field, including the…
We develop a procedure that reorganizes the perturbative expansion in a class of quantum field theories into a stringy amplitude expressed as a sum over two-dimensional geometries. Using Schwinger parametrization and the one-to-one…
In this paper we consider the growth, large fluctuations and memory properties of an affine stochastic functional differential equation with an average functional where the contributions of the average and instantaneous terms are…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We investigate the dynamics of microcapsules in linear shear flow within a reduced model with two degrees of freedom. In previous work for steady shear flow, the dynamic phases of this model, i.e. swinging, tumbling and intermittent…
The duration of activity growths in solar cycles is on average shorter than the duration of its declines. This asymmetry can result from fluctuations in dynamo parameters. A solar dynamo model with fluctuations in the $\alpha$-effect shows…