Related papers: Hyper-Mahler measures via Goncharov-Deligne cyclot…

For a generic one-parameter degeneration of projective hypersurfaces, we show that the periods of the limiting mixed Hodge structure are generated by certain special values of logarithm, Gamma and Dirichlet $L$-functions. Our proof is based…

For a class of orthogonal polynomials related to the $q$-Meixner polynomials corresponding to an indeterminate moment problem we give a one-parameter family of orthogonality measures. For these measures we complement the orthogonal…

Higgs couplings can be measured at a linear collider with high precision. We estimate the uncertainties of such measurements, including theoretical errors. Based on these results we show an extrapolation for a combined analysis at a linear…

This paper develops the use of Dirichlet forms to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis-Hastings random walk samplers) under regularity conditions which are substantially…

We present computational data and heuristic arguments which suggest that given a hyperbolic knot the volume correlates with its determinant, the Mahler measure of its Alexander polynomial and the Mahler measure of the twisted Alexander…

In this paper the discrete Sobolev inner product $$< p,q > =\int p(x) q(x) \,d\mu + \sum_{i=0}^r M_i \, p^{(i)}(c) \, q^{(i)}(c)$$ is considered, where $\mu$ is a finite positive Borel measure supported on an infinite subset of the real…

We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary…

A calculation method for higher-order moments of physical quantities, including magnetization and energy, based on the higher-order tensor renormalization group is proposed. The physical observables are represented by impurity tensors. A…

Using McMullen's Hausdorff dimension algorithm, we study numerically the dimension of the limit set of groups generated by reflections along three geodesics on the hyperbolic plane. Varying these geodesics, we found four minima in the…

We provide a representation of the (signed) BMV-measure by stochastic means and prove positivity of the respective measures in dimension $d=3$ in several non-trivial cases by combinatorial methods.

We use the Wilf-Zeilberger method to prove identities between Mahler measures of polynomials. In particular, we offer a new proof of a formula due to Lal\'{i}n, and we show how to translate the identity into a formula involving elliptic…

A Bayesian re-analysis of published radial velocity data sets is providing evidence for additional planetary candidates. The nonlinear model fitting is accomplished with a new hybrid Markov chain Monte Carlo (HMCMC) algorithm which…

We study a 2+1 dimensional model of superconductors using a 3+1 dimensional gravitational dual theory of a black hole coupled to a scalar field, with negative cosmological constant. In the presence of finite temperature T and a background…

In this work, we introduce a unified method to characterize and measure multipartite entanglement using the framework of thermodynamics. A family of the new entanglement measures is proposed: \textit{ergotropic-gap concentratable…

Adopting the Mahler measure from number theory, we introduce it to toric quiver gauge theories, and study some of its salient features and physical implications. We propose that the Mahler measure is a universal measure for the quiver,…

A time inhomogeneous generalized Mehler semigroup on a real separable Hilbert space ${\mathds{H}}$ is defined through $$ p_{s,t}f(x)=\int_{\mathds{H}} f(U(t,s)x+y)\,\mu_{t,s}(dy), \quad t\geq s, \ x\in{\mathds{H}} $$ for every bounded…

Measurements at hadron colliders rely on large scale quantum chromodynamics (QCD) Monte Carlo (MC) production for interpretation of the data. MC simulations allow testing Standard Model (SM) with more accurate and precise calculations to…

We prove that the expected value and median of the supremum of $L^2$ normalized random holomorphic fields of degree $n$ on $m$-dimensional K\"ahler manifolds are asymptotically of order $\sqrt{m\log n}$. This improves the prior result of…

Using twistor methods we derive a generating function which leads to the hyperk\" ahler metric on a deformation of the Atiyah-Hitchin monopole moduli space. This deformation was first considered by Dancer through the quotient construction…

A Kahler metric is said to be Bochner-Kahler if its Bochner curvature vanishes. This is a nontrivial condition when the complex dimension of the underlying manifold is at least 2. In this article it will be shown that, in a certain…