Related papers: Equidistribution Rates, Closed String Amplitudes, …
Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Francis Brown and Cl\'ement Dupont which states that tree-level amplitudes of closed and open strings are related through the…
We study the asymptotic properties of the conormal cycle of nodal sets associated to a random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian manifold without boundary. In the case where the dimension is odd,…
A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.
We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dimensions. In particular we identify N=1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces…
Perturbative spectra and related factorization properties of one-loop open string amplitudes in the presence of a constant external background B are analysed in detail. While the pattern of the closed string spectrum, obtained after a…
We show that the one loop amplitudes of open and closed string theory in a constant background two-form tensor field are characterized by an effective string tension larger than the fundamental string tension, and by the appearance of…
The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…
We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus. This allows us to write explicit linear relations…
Characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range of statistical applications. To this end, in this paper we introduce a general…
Physical properties of scattering amplitudes are mapped to the Riemann zeta function. Specifically, a closed-form amplitude is constructed, describing the tree-level exchange of a tower with masses $m_n^2 = \mu_n^2$, where…
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…
We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on…
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…
Hidden nonabelian symmetries in nonlinear interactions of radiation with matter are clarified. In terms of a nonabelian potential variable, we construct an effective field theory of self-induced transparency, a phenomenon of lossless…
This work has two main purposes. On the one side we investigate in this work a question of H. Esnault on congruence formula in a construction of H. Esnault and C. Xu for the number of rational points on the closed fiber of a singular model…
We compute the whole asymptotic expansion of the probability that a large uniform labeled graph is connected, and of the probability that a large uniform labeled tournament is irreducible. In both cases, we provide a combinatorial…
We study the spectrum of the Laplacian on the hemisphere with Robin boundary conditions. It is found that the eigenvalues fall into small clusters around the Neumann spectrum, and satisfy a Szeg\H{o} type limit theorem. Sharp upper and…
We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on…
Using general local conservations laws we derive dispersion relations for edge modes in a slab of electron liquid confined by a symmetric potential. The dispersion relations are exact up to $\lambda^{2} q^{2}$, where $q$ is a wave vector…