6 citations · 16 across the 15 of their papers we have counts for
16 papers
Two-sided heat kernel bounds for -Liouville Brownian motion
Sebastian Andres, Naotaka Kajino, Konstantinos Kavvadias +1
Liouville Brownian motion (LBM) is the canonical diffusion process on a Liouville quantum gravity (LQG) surface. In this work, we establish upper and lower bounds for the heat kern…
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…
-Energy forms on fractals: recent progress
Naotaka Kajino, Ryosuke Shimizu
In this article, we survey recent progress on self-similar -energy forms on self-similar fractals, where . While for the notion of such forms coincides wit…
Contraction properties and differentiability of -energy forms with applications to nonlinear potential theory on self-similar sets
Naotaka Kajino, Ryosuke Shimizu
We introduce a new contraction property, which we call the generalized -contraction property, for -energy forms as generalizations of many well-known inequalities, such as $p…
Korevaar-Schoen -energy forms and associated -energy measures on fractals
Naotaka Kajino, Ryosuke Shimizu
We construct good -energy forms on metric measure spaces as pointwise subsequential limits of Besov-type -energy functionals under certain geometric/analytic conditions. Such…
Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
Naotaka Kajino, Mathav Murugan
We study the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion o…
On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates II: Some borderline examples
Naotaka Kajino
We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular Sierpiński gaskets and each of which is equipped with a canonical strongly local…
Two-sided bounds on free energy of directed polymers on strongly recurrent graphs
Naotaka Kajino, Kosei Konishi, Makoto Nakashima
We study the directed polymers in random environment on an infinite graph on which the underlying random walk satisfies sub-Gaussian heat kernel bounds with spectral dime…
On the conformal walk dimension: Quasisymmetric uniformization for symmetric diffusions
Naotaka Kajino, Mathav Murugan
We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact…
An elementary proof that walk dimension is greater than two for Brownian motion on Sierpiński carpets
Naotaka Kajino
We give an elementary self-contained proof of the fact that the walk dimension of the Brownian motion on an arbitrary generalized Sierpiński carpet is greater than two, no proof of…
The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the ergodic-theoretic aspects
Naotaka Kajino
This short survey is aimed at sketching the ergodic-theoretic aspects of the author's recent studies on Weyl's eigenvalue asymptotics for a \emph{"geometrically canonical" Laplacia…
The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the analytic aspects
Naotaka Kajino
This article surveys the analytic aspects of the author's recent studies on the construction and analysis of a "geometrically canonical" Laplacian on circle packing fractals invari…
On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates
Naotaka Kajino, Mathav Murugan
We show that for a strongly local, regular symmetric Dirichlet form over a complete, locally compact geodesic metric space, full off-diagonal heat kernel estimates with walk dimens…
Equivalence of recurrence and Liouville property for symmetric Dirichlet forms
Naotaka Kajino
Given a symmetric Dirichlet form on a (non-trivial) -finite measure space with associated Markovian semigroup $\{T_{t}\}_{t\in(0,…
Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula
Alexander Grigor'yan, Naotaka Kajino
We prove that for a general diffusion process, certain assumptions on its behavior \emph{only within a fixed open subset} of the state space imply the existence and sub-Gaussian ty…
Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions
Sebastian Andres, Naotaka Kajino
The Liouville Brownian motion (LBM), recently introduced by Garban, Rhodes and Vargas and in a weaker form also by Berestycki, is a diffusion process evolving in a planar random ge…