相关论文: Critical dimension of Spectral Triples
In this work we extend the etching model to $d+1$ dimensions. This permits us to investigate its exponents behaviour on higher dimensions, to try to verify the existence of an upper critical dimension for the KPZ equations, with our results…
QCD in $d=4-2\epsilon$ space-time dimensions possesses a nontrivial critical point. Scale invariance usually implies conformal symmetry so that there are good reasons to expect that QCD at the critical point restricted to the gauge…
The essential matrix incorporates relative rotation and translation parameters of two calibrated cameras. The well-known algebraic characterization of essential matrices, i.e. necessary and sufficient conditions under which an arbitrary…
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the…
We consider a class of random graphs, called random brushes, which are constructed by adding linear graphs of random lengths to the vertices of Z^d viewed as a graph. We prove that for d=2 all random brushes have spectral dimension d_s=2.…
We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we will consider the convergence of critical crossing probabilities to Cardy's formula and of the critical exploration path to…
We study natural conditions on essentially discrete spectral triples by which the quantum differential $da$ belongs to the ideal generated by the unit length $ds=D^{-1}$. We also study upper and lower bounds on the singular values of the…
We consider Hardy inequalities in $I R^n$, $n \geq 3$, with best constant that involve either distance to the boundary or distance to a surface of co-dimension $k<n$, and we show that they can still be improved by adding a multiple of a…
In both quantum computing and black hole physics, it is natural to regard some deformations, infinitesimal unitaries, as \emph{easy} and others as \emph{hard}. This has lead to a renewed examination of right-invariant metrics on…
Critical exponents are computed for a variety of twist-2 composite operators, which occur in polarized and unpolarized deep inelastic scattering, at leading order in the 1/N_f expansion. The resulting d-dimensional expressions, which depend…
Given that the scale of quantum gravity is not experimentally accessible, one naturally resorts to mathematical consistency as a measure for a good candidate theory to replace General Relativity at high energies. Reproducing the…
Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.
In the paper we study properties of the set of critical points for self-similar sets. We introduce simple condition that implies at most countably many critical values and we construct a self-similar set with uncountable set of critical…
An action for a string and a particle with two timelike dimensions is proposed and analyzed. Due to new gauge symmetries and associated constraints, the motion of each system in the background of the other is equivalent to effective motion…
Estimates of the fractal dimension $D$ of the set of galaxies in the universe, based on ever improving data sets, tend to settle on $D\approx 2$. This result raised a raging debate due to its glaring contradiction with astrophysical models…
We compute the essential dimension of finite groups of order $\leqslant 63$.
A 1/L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo…
We provide a proof of Connes' formula for a representative of the Hochschild class of the Chern character for (p,\infty)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p\geq 1. We…
We show that there exists a dense set of frequencies with positive Hausdorff dimension for which the Hausdorff dimension of the spectrum of the critical almost Mathieu operator is positive.
This paper complements the results of Andresen et. al "Critical dimension in profile semiparametric estimation" (2014) on profile estimators in semiparametric models. We present two examples. One that illustrates that the smoothness…