相关论文: On a degenerating limit theorem of DeMarco--Faber

For an analytic family $\{f_t\}_{t\in\mathbb{D}^*}$ on the unit punctured disk that meromorphically degenerates at the origin, we show that its limiting measure on an snc model is given by the push forward of the canonical measure attached…

We show that the weak limit of the maximal measures for any degenerating sequence of rational maps on the Riemann sphere must be a countable sum of atoms. For a 1-parameter family f_t of rational maps, we refine this result by showing that…

We consider a meromorphic family of endomorphisms of degree at least 2 of a complex projective space that is parameterized by the unit disk.We prove that the measure of maximal entropy of these endomorphisms converges to the equilibrium…

We study pairs $(f, \Gamma)$ consisting of a non-Archimedean rational function $f$ and a finite set of vertices $\Gamma$ in the Berkovich projective line, under a certain stability hypothesis. We prove that stability can always be attained…

For a certain maximal unipotent family of Abelian varieties over the punctured disc, we show that after a base change, one can complete the family over a disc such that the whole degeneration can be simultaneously balanced embedded into a…

In this short paper, we aim at giving a more conceptual and simpler proof of Rumely's moduli theoretic characterization of type II minimal locus of the resultant function $\operatorname{ordRes}_\phi$ on the Berkovich hyperbolic space for a…

We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can…

In this paper, we prove the existence portion of the Bertram-Feinberg-Mukai Conjecture for an infinite family of new cases using degeneration technique. This not only leads to a substantial improvement of known results but also develops…

In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi's iteration. As applications, we show the existence of weak solutions for possibly degenerate stochastic…

Based on Jaynes' maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered…

The spectral gap of a Markov chain can be bounded by the spectral gaps of constituent "restriction" chains and a "projection" chain, and the strength of such a bound is the content of various decomposition theorems. In this paper, we…

We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account,…

We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges…

The primary goal of this paper is to complete the theory of metric Diophantine approximation initially developed in [Ann. of Math.(2) 166 (2007), p.367-426] for $C^3$ non-degenerate planar curves. With this goal in mind, here for the first…

We study the asymptotic behavior of volume forms on a degenerating family of compact complex manifolds. Under rather general conditions, we prove that the volume forms converge in a natural sense to a Lebesgue-type measure on a certain…

As a consequence of our recently established generalized Schmidt's subspace theorem for closed subschemes in general position, we prove a degeneracy theorem for integral points on the complement of a union of nef effective divisors. A novel…

The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is…

We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…

In this paper, we introduce topological entropy for dynamical systems generated by a single local homeomorphism (Deaconu-Renault systems). More precisely, we generalize Adler, Konheim, and McAndrew's definition of entropy via covers and…

We introduce a "limiting Frobenius structure" attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be…