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Ronkin/Zeta Correspondence

Takashi KomatsuNorio KonnoIwao SatoKohei Sato
Dec 2022
摘要
The Ronkin function was defined by Ronkin in the consideration of the zerosof almost periodic function. Recently, this function has been used in variousresearch fields in mathematics, physics and so on. Especially in mathematics,it has a closed connections with tropical geometry, amoebas, Newton polytopesand dimer models. On the other hand, we have been investigated a new class of zeta functionsfor various kinds of walks including quantum walks by a series of our previouswork on Zeta Correspondence. The quantum walk is a quantum counterpart of therandom walk. In this paper, we present a new relation between the Ronkinfunction and our zeta function for random walks and quantum walks. Firstly weconsider this relation in the case of one-dimensional random walks. Afterwardswe deal with higher-dimensional random walks. For comparison with the case ofthe quantum walk, we also treat the case of one-dimensional quantum walks. Ourresults bridge between the Ronkin function and the zeta function via quantumwalks for the first time.
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