相关论文: Large deviations for Gibbs measures with singular …

In the present paper and the companion paper [8] a probabilistic (statistical mechanical) approach to the study of canonical metrics and measures on a complex algebraic variety X is introduced. On any such variety with positive Kodaira…

This is an invitation to the probabilistic approach for constructing K\"ahler-Einstein metrics on complex projective algebraic manifolds X. The metrics in question emerge in the large N-limit from a canonical way of sampling N points on X,…

In this paper, we study several types of geometric problems related to the Ricci curvature on noncompact complex manifolds, such as the existence of K\"{a}hler-Einstein metrics on complete K\"{a}hler manifolds with negative Ricci curvature,…

We develop a variational calculus for a certain free energy functional on the space of all probability measures on a Kahler manifold X. This functional can be seen as a generalization of Mabuchi's K-energy functional and its twisted…

Let $D$ be a smooth divisor in a compact complex manifold $X$ and let $\beta \in (0,1)$. We show that in any positive co-homology class on $X$ there is a K\"ahler metric with cone angle $2\pi\beta$ along $D$ which has bounded Ricci…

We consider the random point processes on a measure space X defined by the Gibbs measures associated to a given sequence of N-particle Hamiltonians H^{(N)}. Inspired by the method of Messer-Spohn for proving concentration properties for the…

In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and K\"ahler-Einstein metrics of negative Ricci with a cuspidal point. As an application, we…

In the probabilistic construction of K\"ahler-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…

In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…

We construct Kahler-Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2 or if the…

We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar…

Tian initiated the study of incomplete K\"ahler-Einstein metrics on quasi-projective varieties with cone-edge type singularities along a divisor, described by the cone-angle $2\pi(1-\alpha)$ for $\alpha\in (0, 1)$. In this paper we study…

We extend the probabilistic approach for constructing Kahler-Einstein metrics on log Fano manifolds X - involving random point processes - to the case of non-discrete automorphism groups, by breaking the symmetry using a moment map…

Various curvature conditions are studied on metrics admitting a symmetry group. We begin by examining a method of diagonalizing cohomogeneity-one Einstein manifolds and determine when this method can and cannot be used. Examples, including…

In this short note we are concerned with the Kahler-Einstein metrics near cone type log canonical singularities. By two different approaches, we construct a complete Kahler-Einstein metric with negative scalar curvature in a neighborhood of…

We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We…

This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational…

We prove the large deviation principle for the conditional Gibbs measure associated with the focusing Gross Pitaevskii equation in the low temperature regime. This conditional measure is of mixed type, being canonical in energy and…

We introduce new probabilistic and variational constructions of (twisted) K\"ahler-Einstein metrics on complex projective algebraic varieties, drawing inspiration from Onsager's statistical mechanical model of turbulence in two-dimensional…

A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with…