1,092 research outputs found
Ronkin/Zeta Correspondence
The Ronkin function was defined by Ronkin in the consideration of the zeros
of almost periodic function. Recently, this function has been used in various
research fields in mathematics, physics and so on. Especially in mathematics,
it has a closed connections with tropical geometry, amoebas, Newton polytopes
and dimer models.
On the other hand, we have been investigated a new class of zeta functions
for various kinds of walks including quantum walks by a series of our previous
work on Zeta Correspondence. The quantum walk is a quantum counterpart of the
random walk. In this paper, we present a new relation between the Ronkin
function and our zeta function for random walks and quantum walks. Firstly we
consider this relation in the case of one-dimensional random walks. Afterwards
we deal with higher-dimensional random walks. For comparison with the case of
the quantum walk, we also treat the case of one-dimensional quantum walks. Our
results bridge between the Ronkin function and the zeta function via quantum
walks for the first time.Comment: 19 pages. arXiv admin note: substantial text overlap with
arXiv:2202.05966; text overlap with arXiv:2109.07664, arXiv:2104.1028
Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs
We propose a new approach to formally describing the requirement for
statistical inference and checking whether a program uses the statistical
method appropriately. Specifically, we define belief Hoare logic (BHL) for
formalizing and reasoning about the statistical beliefs acquired via hypothesis
testing. This program logic is sound and relatively complete with respect to a
Kripke model for hypothesis tests. We demonstrate by examples that BHL is
useful for reasoning about practical issues in hypothesis testing. In our
framework, we clarify the importance of prior beliefs in acquiring statistical
beliefs through hypothesis testing, and discuss the whole picture of the
justification of statistical inference inside and outside the program logic
Topological Classificaton of Non-Hermitian Gapless Phases: Exceptional Points and Bulk Fermi Arcs
We provide classification of gapless phases in non-Hermitian systems
according to two types of complex-energy gaps: point gap and line gap. We show
that exceptional points, at which not only eigenenergies but also eigenstates
coalesce, are characterized by gap closing of point gaps with nontrivial
topological charges. Moreover, we find that bulk Fermi arcs accompanying
exceptional points are robust because of topological charges for real line
gaps. On the basis of the classification, some examples are also discussed.Comment: 6 pages, 1 figure, 3 tables, submitted to the Proceedings of SCES
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