10 papers
A Central Limit Theorem for High-Temperature SYK Model: A case study on mathematical research using AI and Lean
Yoshinori Kamijima, Shuta Nakajima, Ryoichiro Noda +1
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 hi…
Scaling limit of the collision measure for two-dimensional random walks
Shuta Nakajima, Ryoichiro Noda
We study the scaling limit of the collision measure of two i.i.d. discrete-time random walks on , which records their collision sites and times. This is a critical reg…
Exact Hausdorff measures and fine geometry of collisions of independent Markov processes
Ryoichiro Noda
We study the fine geometry of collision measures associated with independent Markov processes on a common metric measure space. These measures are natural space-time random measure…
Convergence of space-time occupation measures of stochastic processes and its application to collisions
Ryoichiro Noda
We introduce a new perspective on positive continuous additive functionals (PCAFs) of Markov processes, which we call space--time occupation measures (STOMs). This notion provides…
Generalized Kac's moment formula for positive continuous additive functionals of Markov processes
Naotaka Kajino, Ryoichiro Noda
We establish a formula for moments of certain random variables involving positive continuous additive functionals (PCAFs) of standard processes which have absolutely continuous tra…
Continuity of the Revuz correspondence under the absolute continuity condition
Ryoichiro Noda
In this paper, we consider standard processes that admit dual processes and satisfy the absolute continuity condition, i.e., processes possess transition densities. For such proces…
Aging and sub-aging for Bouchaud trap models on resistance metric spaces
Ryoichiro Noda
In this paper, we prove that if a sequence of electrical networks converges in the local Gromov-Hausdorff topology and satisfies a non-explosion condition, then the associated Bouc…
Scaling limits of discrete-time Markov chains and their local times on electrical networks
Ryoichiro Noda
We establish that if a sequence of electrical networks equipped with conductance measures converges in the local Gromov--Hausdorff-vague topology and satisfies certain non-explosio…
Metrization of Gromov-Hausdorff-type topologies on boundedly-compact metric spaces
Ryoichiro Noda
We present a new general framework for metrization of Gromov-Hausdorff-type topologies on non-compact metric spaces. We also give easy-to-check conditions for separability and comp…
Convergence of local times of stochastic processes associated with resistance forms
Ryoichiro Noda
In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain no…