Alexander Hock

collaborators

6 papers

math-ph2026

Universal Correlators on Exponentially Ramified Spectral Curves

Mohamad Alameddine, Alexander Hock

We investigate generalized topological recursion on compact spectral curves admitting exponential, and more generally essential, singularities as ramification points. Exploiting th…

math-ph2026

Geometry of Logarithmic Topological Recursion: Dilaton Equations, Free Energies and Variational Formulas

Alexander Hock, Olivier Marchal, Nicolas Orantin

One of the most important applications of topological recursion concerns spectral curves for which the functions $(x, y)$ defining the spectral curve are allowed to have logarithmic…

math-ph2025

Solution of all quartic matrix models

Harald Grosse, Alexander Hock, Raimar Wulkenhaar

We consider the quartic analogue of the Kontsevich model, which is defined by a measure $exp (- N Tr (E I^¦^{2} + (I^»/4) I^¦^{4})) d I^¦$ on Hermitian $N \times N$ -matrices, where…

math-ph2025

Symplectic (Non-)Invariance of the Free Energy in Topological Recursion

Alexander Hock

Let $F_{g}$ be the free energy derived from Topological Recursion for a given spectral curve on a compact Riemann surface, and let $F_{g}^{\lor}$ be its $x$ - $y$ dual, that is, the free e…

math-ph2025

Blobbed topological recursion from extended loop equations

Alexander Hock, Raimar Wulkenhaar

We consider the $N \times N$ Hermitian matrix model with measure $d I^¼_{E, I^»} (M) = \frac{1}{Z} exp (- \frac{I ^ » N}{4} tr (M^{4})) d I^¼_{E, 0} (M)$ , where $d I^¼_{E, 0}$ is the Gaussian me…

math.CV2025

Symmetry of meromorphic differentials produced by involution identity, and relation to integer partitions

Alexander Hock, Sergey Shadrin, Raimar Wulkenhaar

We prove that meromorphic differentials $ω_{n}^{(0)} (z_{1}, ..., z_{n})$ which are recursively generated by an involution identity are symmetric in all their arguments $z_{1}, ..., z_{n}$ . The p…