Planar maps, circle patterns and 2d gravity

Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point process. We show that this measure can be expressed as: (1) a sum over 3-spanning-trees partitions of the edges of the Delaunay triangulations; (2) the volume form of a K\"ahler metric over the space of Delaunay triangulations, whose prepotential has a simple formulation in term of ideal tessellations of the 3d hyperbolic space; (3) a discretized version (involving finite difference complex derivative operators) of Polyakov's conformal Fadeev-Popov determinant in 2d gravity; (4) a combination of Chern classes, thus also establishing a link with topological 2d gravity.Comment: Misprints corrected and a couple of footnotes added. 42 pages, 17 figure

On the Hausdorff dimension of CAT(κ\kappa) surfaces

We prove that a closed surface with a CAT($\kappa$) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls. We also discuss a connection between this uniformity condition and some results on the dynamics of the geodesic flow for such surfaces. Finally, we give a short proof of topological entropy rigidity for geodesic flow on certain CAT(-1) manifolds.Comment: 13 pages, 3 figure

Identified hadron spectra in Pb-Pb at sqrt(s) = 5.5 TeV: hydrodynamics+pQCD predictions

The single inclusive charged hadron pT spectra in Pb-Pb collisions at the LHC, predicted by a combined hydrodynamics+perturbative QCD (pQCD) approach are presented.Comment: 2 pages, 2 figures. Contribution to "Workshop on Heavy Ion Collisions at the LHC: Last Call for Predictions", Geneva, Switzerland, 14 May - 8 Jun 2007. To appear in J.Phys.

Direct photon spectra in Pb-Pb at sqrt(s) = 5.5 TeV: hydrodynamics+pQCD predictions

The transverse momentum spectra for direct photons produced in Pb-Pb collisions at the LHC, including thermal (hydrodynamics) and prompt (pQCD) emissions are presented.Comment: 2 pages, 2 figures. Contribution to "Workshop on Heavy Ion Collisions at the LHC: Last Call for Predictions", Geneva, Switzerland, 14 May - 8 Jun 2007. To appear in J.Phys.

Interference Networks with Point-to-Point Codes

The paper establishes the capacity region of the Gaussian interference channel with many transmitter-receiver pairs constrained to use point-to-point codes. The capacity region is shown to be strictly larger in general than the achievable rate regions when treating interference as noise, using successive interference cancellation decoding, and using joint decoding. The gains in coverage and achievable rate using the optimal decoder are analyzed in terms of ensemble averages using stochastic geometry. In a spatial network where the nodes are distributed according to a Poisson point process and the channel path loss exponent is $\beta > 2$, it is shown that the density of users that can be supported by treating interference as noise can scale no faster than $B^{2/\beta}$ as the bandwidth $B$ grows, while the density of users can scale linearly with $B$ under optimal decoding