Related papers: Stochastic K\"ahler geometry: from random zeros to…

We introduce a class of almost homogeneous varieties contained in the class of spherical varieties and containing horospherical varieties as well as complete symmetric varieties. We develop K{\"a}hler geometry on these varieties, with…

In their seminal paper, Berman and Boucksom exploited ideas from complex geometry to analyze asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles $L$ over compact, complex manifolds as the power grows. This…

We show how affine and projective special K\"ahler manifolds emerge from the structure of quantization. We quantize them and construct natural (wavefunction) representations for the corresponding coherent states. These in turn are shown to…

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…

In this note, we propose an approach to the study of the analogue for unipotent harmonic bundles of Schmid's Nilpotent Orbit Theorem. Using this approach, we construct harmonic metrics on unipotent bundles over quasi-compact K\"ahler…

The first goal of the article is to solve several fundamental problems in the theory of holomorphic bundles over non-algebraic manifolds: For instance we prove that stability and semi-stability are Zariski open properties in families when…

We study the asymptotic properties of the conormal cycle of nodal sets associated to a random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian manifold without boundary. In the case where the dimension is odd,…

In this paper, by generalizing the concept of balanced metrics, we shall show that Donaldson's asymptotic approximation of balanced metrics for constant scalar curvature cases can be generalized to extremal Kaehler cases.

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary…

Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in K\"ahler geometry, we prove that the slope at infinity…

A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…

We study the distribution of geometrically and topologically nearly geodesic random surfaces in a closed hyperbolic 3-manifold M. In particular, we describe PSL(2,R) invariant measures on the Grassmann bundle G(M) which arise as limits of…

This is a double exposure of the probabilistic construction of Kahler-Einstein metrics on a complex projective algebraic variety X - where the Kahler-Einstein metric emerges from a canonical random point process on X - and the variational…

We consider the relative canonical line bundle $K_{\mathcal{X}/\mathcal{T}}$ and a relatively ample line bundle $(L, e^{-\phi})$ over the total space $ \mathcal{X}\to \mathcal{T}$ of fibration over the Teichm\"uller space by Riemann…

We obtain a class of locally symmetric Kaehler Einstein structures on the cotangent bundle of a Riemannian manifold of negative sectional curvature. Similar results are obtained in the case of a Riemannian manifold of positive sectional…

This paper, the second of a series, deals with the function space of all smooth K\"ahler metrics in any given closed complex manifold $M$ in a fixed cohomology class. The previous result of the second author \cite{chen991} showed that the…

We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…

Over a compact K\"ahler manifold, we provide a Fredholm alternative result for the Lichnerowicz operator associated to a K\"ahler metric with conic singularities along a divisor. We deduce several existence results of constant scalar…

The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted…

After a short discussion of the intimate relation between the generalized statistics and supersymmetry, we review the recent results on the nonlinear supersymmetry obtained in the context of the quantum anomaly problem and of the universal…