Ryokichi Tanaka

activity

20112026

most citedDimension of harmonic measures in hyperbolic spaces

21 citations · 54 across the 16 of their papers we have counts for

collaborators

18 papers

math.PR2026

Drift and joint minimal displacement for groups acting on hyperbolic spaces

Koji Fujiwara, Ryokichi Tanaka

We obtain a uniform lower bound for the drift of random walks on hyperbolic spaces in terms of joint minimal displacement. Our main theorem applies to weakly acylindrical actions o…

math.GR2026

Small growth rates of free groups

Koji Fujiwara, Sang-hyun Kim, Ryokichi Tanaka

We introduce the notion of a Magnus marking for a finite generating set of a group and prove a certain expansion property. Using this property, we determine the second and third sm…

math.PR2022

Non-noise sensitivity for word hyperbolic groups

Ryokichi Tanaka

We show that non-elementary random walks on word hyperbolic groups with finite first moment are not noise sensitive in a strong sense for small noise parameters.

math.DS2022

Invariant measures of the topological flow and measures at infinity on hyperbolic groups

Stephen Cantrell, Ryokichi Tanaka

We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include reg…

math.NT2022

Isogeny graphs on superspecial abelian varieties: Eigenvalues and Connection to Bruhat-Tits buildings

Yusuke Aikawa, Ryokichi Tanaka, Takuya Yamauchi

We study for each fixed integer $g \geq 2$ , for all primes $ℓ$ and $p$ with $ℓ \neq = p$ , finite regular directed graphs associated with the set of equivalence classes of $ℓ$ …

math.DS2021★ 4 cited

The Manhattan curve, ergodic theory of topological flows and rigidity

Stephen Cantrell, Ryokichi Tanaka

For every non-elementary hyperbolic group, we introduce the Manhattan curve associated to any pair of left-invariant hyperbolic metrics which are quasi-isometric to a word metric.…

math.PR2020

Glauber-Exclusion dynamics : rapid mixing regime

Ryokichi Tanaka, Kenkichi Tsunoda

We show that for any attractive Glauber-Exclusion process on the one-dimensional lattice of size $N$ with periodic boundary condition, if the corresponding hydrodynamic limit equat…

math.DS2019★ 2 cited

Topological flows for hyperbolic groups

Ryokichi Tanaka

We show that for every non-elementary hyperbolic group the Bowen-Margulis current associated with a strongly hyperbolic metric forms a unique group-invariant Radon measure class of…

math.DG2019★ 2 cited

Uniformizing surfaces via discrete harmonic maps

Toru Kajigaya, Ryokichi Tanaka

We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Diric…

math.PR2018

Cutoff for product replacement on finite groups

Yuval Peres, Ryokichi Tanaka, Alex Zhai

We analyze a Markov chain, known as the product replacement chain, on the set of generating $n$ -tuples of a fixed finite group $G$ . We show that as $n \to \infty$ , the tota…

cond-mat.soft2018★ 10 cited

Solitons in one-dimensional mechanical linkage

Koji Sato, Ryokichi Tanaka

It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes…

math.GR2017★ 2 cited

Random walks on the discrete affine group

Jérémie Brieussel, Ryokichi Tanaka, Tianyi Zheng

We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of…

math.PR2016★ 21 cited

Dimension of harmonic measures in hyperbolic spaces

Ryokichi Tanaka

We show exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under finite first moment condition, and establish the dimensi…

math.PR2015

Random Dirichlet series arising from records

Ron Peled, Yuval Peres, Jim Pitman +1

We study the distributions of the random Dirichlet series with parameters $(s, β)$ defined by $S = n = 1 \sum \infty \frac{I _{n}}{n ^{s}},$ where $(I_{n})$ is a sequence of independent…

math.PR2015

A note on a local ergodic theorem for an infinite tower of coverings

Ryokichi Tanaka

This is a note on a local ergodic theorem for a symmetric exclusion process defined on an infinite tower of coverings, which is associated with a finitely generated residually fini…

math.PR2014★ 9 cited

Hausdorff spectrum of harmonic measure

Ryokichi Tanaka

For every non-elementary hyperbolic group, we show that for every random walk with finitely supported admissible step distribution, the associated entropy equals the drift times th…

math.PR2013

Discrete random walks on the group Sol

Jérémie Brieussel, Ryokichi Tanaka

The harmonic measure $ν$ on the boundary of the group $S o l$ associated to a discrete random walk of law $μ$ was described by Kaimanovich. We investigate when it is absolutely conti…

math.PR2011★ 4 cited

Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices

Ryokichi Tanaka

We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map.…