1. D. A. Croydon, T. Kato, M. Sasada, and S. Tsujimoto, Dynamics of the box-ball system
with random initial conditions via Pitman’s transformation, to appear in Mem. Amer.
Math. Soc., preprint appears at arXiv:1806.02147, 2018.
2. D. A. Croydon and M. Sasada, Duality between box-ball systems of finite box and/or
carrier capacity, to appear in RIMS Kˆ
okyˆ
uroku Bessatsu, preprint appears at
arXiv:1905.00189, 2019.
3.
, Invariant measures for the box-ball system based on stationary Markov chains
and periodic Gibbs measures, J. Math. Phys. 60 (2019), no. 8, 083301, 25.
4. B. Doyon, Lecture notes on generalised hydrodynamics, preprint appears at
arXiv:1912.08496, 2019.
5. B. Doyon, H. Spohn, and T. Yoshimura, A geometric viewpoint on generalized hydrodynamics, Nuclear Phys. B 926 (2018), 570–583.
6. G. A. El, The thermodynamic limit of the Whitham equations, Phys. Lett. A 311
(2003), no. 4-5, 374–383.
7. G. A. El and A. M. Kamchatnov, Kinetic equation for a dense soliton gas, Phys. Rev.
Lett. 95 (2005), no. 20, 204101, 4.
8. G. A. El, A. M. Kamchatnov, M. V. Pavlov, and S. A. Zykov, Kinetic equation for
a soliton gas and its hydrodynamic reductions, J. Nonlinear Sci. 21 (2011), no. 2,
151–191.
9. P. A. Ferrari and D. Gabrielli, BBS invariant measures with independent soliton components, preprint appears at arXiv:1812.02437, 2018.
10.
, Box-ball system: soliton and tree decomposition of excursions, preprint appears at arXiv:1906.06405, 2019.
11. P. A. Ferrari, C. Nguyen, L. Rolla, and M. Wang, Soliton decomposition of the box-ball
system, preprint appears at arXiv:1806.02798, 2018.
12. R. Inoue, A. Kuniba, and T. Takagi, Integrable structure of box-ball systems: crystal,
Bethe ansatz, ultradiscretization and tropical geometry, J. Phys. A 45 (2012), no. 7,
073001, 64.
13. S. Kakei, J. J. C. Nimmo, S. Tsujimoto, and R. Willox, Linearization of the box-ball
system: an elementary approach, J. Integrable Syst. 3 (2018), no. 1, xyy002, 32.
14. C. Kipnis and C. Landim, Scaling limits of interacting particle systems, Grundlehren
der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 320, Springer-Verlag, Berlin, 1999.
15. K. Kondo, Dynamics of the multicolor box-ball system with random initial conditions
via Pitman transformation, forthcoming, 2020.
A Self-archived copy in
Kyoto University Research Information Repository
https://repository.kulib.kyoto-u.ac.jp
GENERALIZED HYDRODYNAMIC LIMIT FOR THE BOX-BALL SYSTEM
38
16. A. Kuniba and H. Lyu, Large deviations and one-sided scaling limit of multicolor
box-ball system, to appear in J. Stat. Phys., preprint appears at arXiv:1808.08074,
2019.
17. A. Kuniba, H. Lyu, and M. Okado, Randomized box-ball systems, limit shape of rigged
configurations and thermodynamic Bethe ansatz, Nuclear Phys. B 937 (2018), 240–
271.
18. A. Kuniba, G. Misguich, and V. Pasquier, Generalized hydrodynamics in box-ball system, forthcoming, 2020.
19. L. Levine, H. Lyu, and J. Pike, Double jump phase transition in a soliton cellular
automaton, preprint appears at arXiv:1706.05621, 2017.
20. J. Lewis, H. Lyu, P. Pylvavskyy, and A. Sen, Scaling limit of soliton lengths in a
multicolor box-ball system, preprint appears at arXiv:1911.04458, 2019.
21. H. Spohn, Generalized Gibbs ensembles of the classical Toda chain, preprint appears
at arXiv:1902.07751, 2019.
22. D. Takahashi and J. Satsuma, A soliton cellular automaton, J. Phys. Soc. Japan 59
(1990), 3514–3519.
23. S. Tsujimoto and R. Hirota, Ultradiscrete KdV equation, J. Phys. Soc. Japan 67
(1998), no. 6, 1809–1810.
24. V. E. Zakharov, Kinetic equation for solitons, Sov. Phys. JETP 33 (1971), no. 3,
538–541.
Research Institute for Mathematical Sciences, Kyoto University, Kyoto
606-8502, Japan
Email address: croydon@kurims.kyoto-u.ac.jp
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1,
Komaba, Meguro-ku, Tokyo, 153–8914, Japan
Email address: sasada@ms.u-tokyo.ac.jp
...
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