The probabilistic vs the quantization approach to Kahler-Einstein geometry

In the probabilistic construction of Kahler-Einstein metrics on a complex projective algebraic manifold X-involving random point processes on X-a key role is played by the partition function. In this work a new quantitative bound on the partition function is obtained. It yields, in particular, a new direct analytic proof that X admits a Kahler-Einstein metrics if it is uniformly Gibbs stable. The proof makes contact with the quantization approach to Kahler-Einstein geometry.

Automated summary

In this research, a new quantitative bound on the partition function is obtained, which plays a key role in the probabilistic construction of Kahler-Einstein metrics on a complex projective algebraic manifold X involving random point processes on X. This result leads to a new direct analytic proof that X admits a Kahler-Einstein metrics if it is uniformly Gibbs stable, and it also connects with the quantization approach to Kahler-Einstein geometry.