math-ph papers | Gist.Science

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

🔢 mathematics

The skew Brownian permuton: a new universality class for random constrained permutations

This paper introduces the skew Brownian permuton, a new two-parameter family of random permutons constructed via flows of solutions to skew perturbed Tanaka equations driven by correlated Brownian excursions, which unifies the Baxter and biased Brownian separable permutons as special cases and establishes a direct continuum-level connection between constrained permutations and Liouville quantum gravity spheres decorated with Schramm-Loewner evolution curves.

Jacopo Borga2026-09-30

🔬 physics

Permutons, meanders, and SLE-decorated Liouville quantum gravity

This paper introduces a class of random permutons constructed from space-filling Schramm-Loewner evolution curves on Liouville quantum gravity surfaces, characterizing their geometric properties, proving the sublinear length of their longest increasing subsequences for various pattern-avoiding permutations, and conjecturing their role as the scaling limit of uniform meandric permutations.

Jacopo Borga, Ewain Gwynne, Xin Sun2026-09-30

🔢 mathematics

On the geometry of uniform meandric systems

This paper conjectures that the scaling limit of a uniform random meandric system corresponds to a Liouville quantum gravity sphere decorated by an SLE $_8$ curve and a CLE $_6$ , and provides rigorous proofs of several geometric properties, such as the existence of macroscopic loops and the uniqueness of infinite paths in boundary-modified versions, that support this conjecture.

Jacopo Borga, Ewain Gwynne, Minjae Park2026-09-30

🔢 mathematics

Superized Leznov-Saveliev equations as the zero-curvature condition on a reduced connection

This paper interprets superized Leznov-Saveliev equations of Type 1 as zero-curvature conditions on reduced connections over $OSp(1|2)$ -orbits in $N=1$ extended Minkowski superspace, thereby generalizing the geometric framework to $N>1$ cases while highlighting the distinct mathematical challenges and solution methods associated with Type 2 equations and infinite-dimensional algebras.

Dimitry Leites2026-09-30

⚛️ high-energy theory

Free Probability in a Minimal Quantum Circuit Model

This paper establishes that higher-order out-of-time-order correlators (OTOCs) in a minimal quantum circuit model decay exponentially and approach free independence at late times, a phenomenon characterized by a higher-order influence matrix that links the system's dynamics to free cumulants and the eigenstate thermalization hypothesis.

Felix Fritzsch, Pieter W. Claeys2026-09-30

🔢 mathematics

Convergence of the KMP model to the KPZ equation

This paper proves that the Kipnis-Marchioro-Presutti (KMP) process converges to the Kardar-Parisi-Zhang (KPZ) equation in the long-time limit by identifying the process with a stochastic flow of kernels and applying recent results on random walks in random environments.

Guillaume Barraquand, Francesco Casini2026-09-30

🔢 mathematics

Uniform Hyperbolicity, Bandgaps and Edge Modes in Aperiodic Systems of Subwavelength Resonators

This paper employs the formalism of uniform hyperbolicity and a propagation matrix framework to rigorously characterize the spectral gaps and edge modes of aperiodic one-dimensional arrays of subwavelength resonators, extending strict multicone criteria and spectral bounds from bi-infinite to semi-infinite and finite systems.

Habib Ammari, Clemens Thalhammer, Alexander Uhlmann2026-09-30

🔢 mathematics

Wave-Particle Decomposition for Kinetic Equations II: Full Boltzmann equation

This paper extends the wave-particle decomposition method to the full Boltzmann equation, creating an exact multiscale system that bridges kinetic and hydrodynamic regimes and demonstrates significantly faster convergence than conventional iterative schemes across rarefied to continuum flow conditions.

Chang Liu, Kun Xu2026-09-30

🌀 nonlinear sciences

Generalized Charlier Recurrence Coefficients: Hankel Formulas, Laguerre--Freud Dynamics, and Painlevé V Connections

This paper investigates the monic recurrence coefficients of generalized Charlier polynomials associated with a specific discrete weight by characterizing them through Hankel determinants, Laguerre--Freud dynamical systems, and Painlevé V connections, while providing numerical validation of their asymptotic behavior.

Mahouton Norbert Hounkonnou2026-09-30

🔢 mathematics

Asymptotically Optimal Mixed-State Cloning

This paper determines the asymptotic global fidelities for cloning generic mixed states with simple full-rank spectra, proving that the optimal root fidelity converges to a specific product formula as the ratio of outputs to inputs approaches a constant greater than one.

Jiani Fei, Jinzhao Wang2026-09-30

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