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Large Deviation Statistics Derived from First Passage Times—Inspired by Shishi-odoshi—

Kenta Yamada^1,3 and Syuji Miyazaki^2,3*

¹Kyoto-City Horikawa High School, Shibou-Horikawa-Machi 622-2, Nakagyo-ku, Kyoto 604-8254, Japan
²Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
³ELCAS Kyoto University, http://elcas.kyoto-u.ac.jp/
*E-mail address: syuji@acs.i.kyoto-u.ac.jp

(Received February 14, 2016; Accepted April 27, 2016)

Abstract. Shishi-odoshi is a traditional device found in Japanese gardens composed of a bamboo tube that when filled with water revolves to empty and makes a clanking sound. It consists of a water-filled bamboo tube which clacks against a stone when emptied, and the sound scares beasts and birds from gardens. For a fluctuating flow rate, intervals between the clacks are distributed. The flow rate per unit time and distribution function of the clack interval can be respectively identified as a velocity of a random walker and first passage time distribution. The rate function of the flow rate per unit time is derived not according to its definition, but by use of the distribution function of a first passage time. Difficulties in applying this novel idea to various actual water flows are disscussed. Experimental verification might be easier for a diffusion system than for water flow.

Keywords: Shishi-odoshi, Large Deviation, Rate Function, First Passage Time