Related papers: The expansion for the overlap function

This chapter introduces a variety of spin glass models, beyond the simple Sherrington-Kirkpatrick (SK) version, that have led to enriched understanding and application.

For two-dimensional, immersed closed surfaces $f:\Sigma \to \R^n$, we study the curvature functionals $\mathcal{E}^p(f)$ and $\mathcal{W}^p(f)$ with integrands $(1+|A|^2)^{p/2}$ and $(1+|H|^2)^{p/2}$, respectively. Here $A$ is the second…

The aim of the present work is to exhibit a new proof of the explicit spectral expansion for the fourth moment of the Riemann zeta-function that was established by the second named author a decade ago. Our proof is new, particularly in the…

A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\lambda$ is obtained for all $\lambda \in \mathfrak a^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\lambda$ away from the walls of a Weyl chamber are…

In this paper, we show that on a compact K\"ahler manifold the Calabi flow can be extended as long as some space-time $L^p$ integrals of the scalar curvature are bounded.

We determine the free field hypercubic Dirac operator which is optimally close to satisfying the Ginsparg-Wilson relation. Inserting this operator into the overlap formula, we show that the analytic locality bound on the resulting overlap…

In this paper we prove a gap theorem for K\"ahler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author. We also prove a Liouville theorem for…

In this work, an extension of two-point Ostrowski's formula for $n$-times differentiable functions is proved. A generalization of Taylor formula is deduced. An identity of Fink type for this extension is provided. Error estimates for the…

We find the general form of supersymmetric invariant two point functions. By imposing supersymmetric positivity we obtain the general supersymmetric K\"allen-Lehmann representation.

We describe an explicit construction of approximate Ginsparg-Wilson fermions for QCD. We use ingredients of perfect action origin, and further elements. The spectrum of the lattice Dirac operator reveals the quality of the approximation. We…

We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…

In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…

This paper is the sequel of the paper "Continuity of volumes on arithmetic varieties", in which we established the arithmetic volume function of smooth hermitian Q-invertible sheaves and proved its continuity. The continuity of the volume…

We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined…

In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension $d\geq1$, which generalizes the extension theorem for the mean curvature flow…

We compute the second moment of the Riemann zeta function for shifted arguments over a domain that extends the ones in the literature. We use the Riemann-Siegel formula for the error term in the approximate functional equation and take the…

We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The…

The overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, realizes exact chiral symmetry on the lattice without any unphysical doubler modes. To perform the path integrals, one should, however, note that the overlap fermion…

We prove existence of all moments of the multiplicative coalescent at all times. We obtain as byproducts a number of related results which could be of general interest. In particular, we show the finiteness of the second moment of the $l^2$…

In our previous work \cite{PTA2} we calculated the overlap reduction function for the tensor polarization without employing the short wavelength approximation, this was done by obtaining a power series of nested sums which is valid for all…