Does the galaxy correlation length increase with the sample depth?

We have analyzed the behavior of the correlation length, $r_0$, as a function of the sample depth by extracting from the CfA2 redshift survey volume--limited samples out to increasing distances. For a fractal distribution, the value of $r_0$ would increase with the volume occupied by the sample. We find no linear increase for the CfA2 samples of the sort that would be expected if the Universe preserved its small scale fractal character out to the distances considered (60--100\hmpc). The results instead show a roughly constant value for $r_0$ as a function of the size of the sample, with small fluctuations due to local inhomogeneities and luminosity segregation. Thus the fractal picture can safely be discarded.Comment: Accepted for publication in ApJ

A Gluing Construction Regarding Point Particles in General Relativity

We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled "point-particle" limits analogous to those of Gralla and Wald ("A rigorous derivation of gravitational self-force," Class. Quantum Grav. 2008). In particular, we produce examples of initial data which generalize Schwarzschild - de Sitter initial data and gluing theorems of IMP-type

Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

Directed Branched Polymer near an Attractive Line

We study the adsorption-desorption phase transition of directed branched polymer in $d+1$ dimensions in contact with a line by mapping it to a $d$ dimensional hard core lattice gas at negative activity. We solve the model exactly in 1+1 dimensions, and calculate the crossover exponent related to fraction of monomers adsorbed at the critical point of surface transition, and we also determine the density profile of the polymer in different phases. We also obtain the value of crossover exponent in 2+1 dimensions and give the scaling function of the sticking fraction for 1+1 and 2+1 dimensional directed branched polymer.Comment: 19 pages, 4 figures, accepted for publication in J. Phys. A:Math. Ge

Damping Rates and Mean Free Paths of Soft Fermion Collective Excitations in a Hot Fermion-Gauge-Scalar Theory

We study the transport coefficients, damping rates and mean free paths of soft fermion collective excitations in a hot fermion-gauge-scalar plasma with the goal of understanding the main physical mechanisms that determine transport of chirality in scenarios of non-local electroweak baryogenesis. The focus is on identifying the different transport coefficients for the different branches of soft collective excitations of the fermion spectrum. These branches correspond to collective excitations with opposite ratios of chirality to helicity and different dispersion relations. By combining results from the hard thermal loop (HTL) resummation program with a novel mechanism of fermion damping through heavy scalar decay, we obtain a robust description of the different damping rates and mean free paths for the soft collective excitations to leading order in HTL and lowest order in the Yukawa coupling. The space-time evolution of wave packets of collective excitations unambiguously reveals the respective mean free paths. We find that whereas both the gauge and scalar contribution to the damping rates are different for the different branches, the difference of mean free paths for both branches is mainly determined by the decay of the heavy scalar into a hard fermion and a soft collective excitation. We argue that these mechanisms are robust and are therefore relevant for non-local scenarios of baryogenesis either in the Standard Model or extensions thereof.Comment: REVTeX, 19 pages, 4 eps figures, published versio

Holonomy of Einstein Lorentzian manifolds

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp., vacuum Einstein) Lorentzian manifold, the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.Comment: Dedicated to to Mark Volfovich Losik on his 75th birthday. This version is an extended part of the previous version; another part of the previous version is extended and submitted as arXiv:1001.444

A study of logarithmic corrections and universal amplitude ratios in the two-dimensional 4-state Potts model

Monte Carlo (MC) and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the two-dimensional 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed and an approach is proposed in order to account numerically for these corrections in the determination of critical amplitudes. Accurate estimates of universal amplitude ratios $A_+/A_-$, $\Gamma_+/\Gamma_-$, $\Gamma_T/\Gamma_-$ and $R_C^\pm$ are given, which arouse new questions with respect to previous works