arXiv subjects

Hayate Suda

Publications and source records attributed to Hayate Suda.

6 recordsLinked to original sources

arXiv2024

Scaling limits of solitons in the box-ball system

We study the space-time scaling limits of solitons in the box-ball system with random initial distribution. In particular, we show that any recentered tagged soliton converges to a Brownian motion in the diffusive space-time scale, and also prove the large deviation principle for the tagged soliton under certain shift-ergodic invariant distributions, including Bernoulli product measures and two-sided Markov distributions. Furthermore, in the diffusive space-time scaling, we show that two tagged solitons converge to the same Brownian motion even if they are macroscopically far apart.

math.PR↗

arXiv2023

Seat number configuration of the box-ball system, and its relation to the 10-elimination and invariant measures

The box-ball system (BBS) is a soliton cellular automaton introduced in [TS], and it is known that the dynamics of the BBS can be linearized by several methods. Recently, a new linearization method, called the seat number configuration, was introduced in [MSSS]. In this paper, we develop this method further by introducing the $k$-skip map, which is a natural operation on the seat number configuration. From the soliton point of view, this map lowers the height of each soliton by $k$. We first show that the $k$-skip map shifts the seat number configuration and that, for finite ball configurations on the half-line, the 1-skip map coincides with the 10-elimination introduced in [MIT]. We then extend the seat number configuration and the $k$-skip map to the BBS on the whole-line. Finally, we study the distribution of the $k$-skipped configuration under the invariant measures introduced in [FG]. As an application, we compute expectations of the carriers with seat numbers, which are related to the stationary current and the effective velocity of solitons.

math.CO↗

arXiv2022

Relationships between two linearizations of the box-ball system : Kerov-Kirillov-Reshetikhin bijection and slot configuration

The box-ball system (BBS), which was introduced by Takahashi and Satsuma in 1990, is a soliton cellular automaton. Its dynamics can be linearized by a few methods, among which the best known is the Kerov-Kirillov-Reshetikhin (KKR) bijection using rigged partitions. Recently a new linearization method in terms of "slot configurations" was introduced by Ferrari-Nguyen-Rolla-Wang, but its relations to existing ones have not been clarified. In this paper we investigate this issue and clarify the relation between the two linearizations. For this we introduce a novel way of describing the BBS dynamics using a carrier with seat numbers. We show that the seat number configuration also linearizes the BBS and reveals explicit relations between the KKR bijection and the slot configuration. In addition, by using these explicit relations, we also show that even in case of finite carrier capacity the BBS can be linearized via the slot configuration.

math.CO↗

arXiv2021

Superballistic and superdiffusive scaling limits of stochastic harmonic chains with long-range interactions

We consider one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials which have polynomial decay rate $|x|^{-\theta}, x \to \infty, \theta > 1$ where $x \in \mathbb{Z}$ is the interaction range. The dynamics conserve total momentum, total length and total energy. We prove that the systems evolve macroscopically on superballistic space-time scale $(y \varepsilon^{-1}, t \varepsilon^{- \frac{\theta - 1}{2}})$ when $1 < \theta < 3$, $(y \varepsilon^{-1}, t \varepsilon^{-1} \sqrt{- \log(\varepsilon^{-1})}^{-1})$ when $\theta = 3$, and ballistic space-time scale $(y \varepsilon^{-1}, t \varepsilon^{-1})$ when $\theta > 3$. Combining our results and the results in [10], we show the existence of two different space-time scales on which the systems evolve. In addition, we prove scaling limits of recentered normal modes of superballistic wave equations, which are analogues of Riemann invariants and capture fluctuations around characteristics. The space-time scale is superdiffusive when $2 < \theta \le 4$ and diffusive when $\theta > 4$.

math-ph↗

arXiv2019

A family of fractional diffusion equations derived from stochastic harmonic chains with long-range interactions

We consider one-dimensional infinite chains of harmonic oscillators with stochastic perturbations and long-range interactions which have polynomial decay rate $|x|^{-θ}, x \to \infty, θ> 1$, where $x \in \mathbb{Z}$ is the interaction range. We prove that if $2< θ\le 3$, then the time evolution of the macroscopic thermal energy distribution is superdiffusive and governed by a fractional diffusion equation with exponent $\frac{3}{7-θ}$, while if $θ> 3$, then the exponent is $\frac{3}{4}$. The threshold is $ θ= 3$ because the derivative of the dispersion relation diverges as $k \to 0$ when $θ\le 3$.

math.PR↗

arXiv2018

5/6-Superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field

We consider a one-dimensional infinite chain of coupled charged har- monic oscillators in a magnetic field with a small stochastic perturbation of order $\epsilon$. We prove that for a space-time scale of order $\epsilon$^{-1} the density of energy distribution (Wigner distribution) evolves according to a linear phonon Boltzmann equation. We also prove that an appropriately scaled limit of solutions of the lin- ear phonon Boltzmann equation is a solution of the fractional diffusion equation with exponent 5/6.

math.PR↗