Mathematics – Complex Variables
Scientific paper
2008-12-22
Mathematics
Complex Variables
v2: 36 pages. Major revision, the main new features are: (1) a second proof of the LDP is added which uses the abstract G\"art
Scientific paper
We study determinantal random point processes on a compact complex manifold X associated to an Hermitian metric on a line bundle over X and a probability measure on X. Physically, this setup describes a free fermion gas on X subject to a U(1)- gauge field and when X is the Riemann sphere it specializes to various random matrix ensembles. It is shown that, in the many particle limit, the empirical random measures on X converge exponentially towards the deterministic pluripotential equilibrium measure, defined in terms of the Monge-Ampere operator of complex pluripotential theory. More precisely, a large deviation principle (LDP) is established with a good rate functional. We also express the LDP in terms of the Ray-Singer analytic torsion and the exponentially small eigenvalues of dbar-Laplacians. This can be seen as an effective bosonization formula, generalizing the previously known formula in the Riemann surface case to higher dimensions and the paper is concluded with a heuristic quantum field theory intepretation of the resulting effective boson-fermion correspondence.
No associations
LandOfFree
Determinantal point processes and fermions on complex manifolds: large deviations and bosonization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Determinantal point processes and fermions on complex manifolds: large deviations and bosonization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Determinantal point processes and fermions on complex manifolds: large deviations and bosonization will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-539366