arXiv subjects

Marco Vergamini

Publications and source records attributed to Marco Vergamini.

4 recordsLinked to original sources

arXiv2026

Green currents of holomorphic correspondences on compact Kähler manifolds

Consider a holomorphic correspondence $f$ on a compact Kähler manifold $X$ of dimension $k$. Let $1\le q\le k$ be any integer such that the dynamical degrees of $f$ satisfy $d_{q-1}<d_q$. We construct the Green currents $T_c$ of $f$ associated with the classes $c$ belonging to the dominant eigenspace for the action of $f^*$ on $H^{q,q}(X,\mathbb{R})$. We also show that the super-potential of $T_c$ is $\log$-Hölder-continuous. When $f$ has simple action on cohomology and its graph satisfies an assumption on the local multiplicity, we prove the exponential equidistribution of all positive closed currents towards the main Green current, i.e., the only one associated to the unique maximal degree $d_q$.

math.CV↗

arXiv2026

$\log$-Hölder regularity of currents and equidistribution towards Green currents

Let $f$ be an endomorphism of a projective space or an automorphism of a compact Kähler manifold. We prove that the pull-backs of currents under the iterates of $f$ converge exponentially fast to the Green currents when tested at $\log$-Hölder-continuous observables whose $\mathrm{dd^c}$'s have bounded mass.

math.CV↗

arXiv2025

Mixing and CLT for Hénon-Sibony maps: plurisubharmonic observables

Let $f$ be a complex Hénon map and $μ$ its unique measure of maximal entropy. We prove that $μ$ is exponentially mixing of all orders for all (not necessarily bounded) plurisubharmonic observables, and that all plurisubharmonic functions satisfy the central limit theorem with respect to $μ$. Our results hold more generally for every Hénon-Sibony map on $\mathbb{C}^k$.

math.CV↗

arXiv2025

Exponential mixing of all orders on Kähler manifolds: (quasi-)plurisubharmonic observables

Let $f$ be a holomorphic automorphism of a compact Kähler manifold with simple action on cohomology and $μ$ its unique measure of maximal entropy. We prove that $μ$ is exponentially mixing of all orders for all d.s.h.\ observables, i.e., functions that are locally differences of plurisubharmonic functions. As a consequence, every d.s.h.\ observable satisfies the central limit theorem with respect to $μ$.

math.CV↗