Convergence of combinatorial gravity

Combinatorial dynamics in quantum gravity

We describe the application of methods from the study of discrete dynamical systems to the study of histories of evolving spin networks. These have been found to describe the small scale structure of quantum general relativity and extensions of them have been conjectured to give background independent formulations of string theory. We explain why the the usual equilibrium second order critical ...

Strong convergence on weakly logarithmic combinatorial assemblies

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the author’s analytic approach, we generalize the so-called Fundamental Lemma giving independent process approximation in the total variation distance of the compone...

Combinatorial quantisation of Euclidean gravity in three dimensions

In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson struc...

On Convergence of Evolutionary Computation for Stochastic Combinatorial Optimization

Extending Rudolph’s works on the convergence analysis of evolutionary computation (EC) for deterministic combinatorial optimization problems (COPs), this brief paper establishes a probability one convergence of some variants of explicit-averaging EC to an optimal solution and the optimal value for solving stochastic COPs.

Improving convergence of combinatorial optimization meta-heuristic algorithms