arXiv subjects

Kôhei Sasaya

Publications and source records attributed to Kôhei Sasaya.

6 recordsLinked to original sources

arXiv2026

A Central Limit Theorem for High-Temperature SYK Model

The Sachdev--Ye--Kitaev (SYK) model is a quantum many-body model of Majorana fermions with all-to-all random interactions. It has attracted wide interest in condensed matter and high-energy physics as a solvable model of non-Fermi liquids and holography. Fix an even integer $q\geq4$, and let $Z_N(β)$ be the partition function of the Gaussian $q$-body SYK model. We prove that for all sufficiently small inverse temperatures $β> 0$, there exists $ρ=ρ(β)>0$ such that \[ N^{q/2 -1}(\log Z_N(β)-\mathbb{E}[\log Z_N(β)]) \Longrightarrow \mathcal{N}(0,ρ^2). \] In addition to the mathematical results, we discuss how the proofs were developed and refined through interaction between human researchers and AI, and we describe the subsequent formalization of the main arguments in Lean 4. This work thus serves as a case study of a research workflow that integrates human insight, AI-assisted exploration, iterative proof refinement, and formal verification.

math.PR↗

arXiv2026

Construction of $p$-energy measures associated with strongly local $p$-energy forms

We construct canonical $p$-energy measures associated with strongly local $p$-energy forms without assuming self-similarity. Here, $p$-energy forms are $L^p$-analogues of Dirichlet forms, which have recently been studied mainly on fractals. Furthermore, we prove that these measures satisfy the chain and Leibniz rules, and that such "good" energy measures are unique. A key ingredient is a $p$-energy analogue of Le Jan's domination principle. Moreover, we show that the Korevaar$-$Schoen-type $p$-energy measures defined by Alonso-Ruiz and Baudoin (2025, Nonlinear Anal.) coincide with our canonical $p$-energy measures.

math.FA↗

arXiv2023

Some relation between spectral dimension and Ahlfors regular conformal dimension on infinite graphs

The spectral dimension $d_s$ of a weighted graph is an exponent associated with the asymptotic behavior of the random walk on the graph. The Ahlfors regular conformal dimension $\dim_\mathrm{ARC}$ of the graph distance is a quasisymmetric invariant, where quasisymmetry is a well-studied property of homeomorphisms between metric spaces. In this paper, we give a typical example of a fractal-like graph with $d_s<\dim_\mathrm{ARC}<2$ and prove a sufficient condition for $\dim_\mathrm{ARC}\le d_s<2.$

math.PR↗

arXiv2022

Some inequalities between Ahlfors regular conformal dimension and spectral dimensions for resistance forms

Quasisymmetric maps are well-studied homeomorphisms between metric spaces preserving annuli, and the Ahlfors regular conformal dimension $\dim_\mathrm{ARC}(X,d)$ of a metric space $(X,d)$ is the infimum over the Hausdorff dimensions of the Ahlfors regular images of the space by quasisymmetric transformations. For a given regular Dirichlet form with the heat kernel, the spectral dimension $d_s$ is an exponent which indicates the short-time asymptotic behavior of the on-diagonal part of the heat kernel. In this paper, we consider the Dirichlet form induced by a resistance form on a set $X$ and the associated resistance metric $R$. We prove $\dim_\mathrm{ARC}(X,R)\le \overline{d_s}<2$ for $\overline{d_s}$, a variation of $d_s$ defined through the on-diagonal asymptotics of the heat kernel. We also give an example of a resistance form whose spectral dimension $d_s$ satisfies the opposite inequality $d_s<\dim_\mathrm{ARC}(X,R)<2.$

math.MG↗

arXiv2021

Systems of Dyadic Cubes of Complete, Doubling, Uniformly Perfect Metric Spaces without Detours

Systems of dyadic cubes are the basic tools of harmonic analysis and geometry, and this notion had been extended to general metric spaces. In this paper, we construct systems of dyadic cubes of complete, doubling, uniformly perfect metric spaces, such that for any two points in the metric space, there exists a chain of three cubes whose diameters are comparable to the distance of the points. We also give an application of our construction to previous research of potential analysis and geometry of metric spaces.

math.MG↗

arXiv2020

Ahlfors Regular Conformal Dimension of Metrics on Infinite Graphs and Spectral Dimension of the Associated Random Walks

Quasisymmetry is a well-studied property of homeomorphisms between metric spaces, and Ahlfors regular conformal dimension is a quasisymmetric invariant. In the present paper, we consider the Ahlfors regular conformal dimension of metrics on infinite graphs, and show that this notion coincides with the critical exponent of $p$-energies. Moreover, we give a relation between the Ahlfors regular conformal dimension and the spectral dimension of a graph.

math.PR↗