Determinantal point processes and fermions on complex manifolds: large deviations and bosonization

Mathematics – Complex Variables

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

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

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

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.

Rate now

     

Profile ID: LFWR-SCP-O-539366

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.