Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665712015AN EXPLICIT EFFECT OF NON-SYMMETRY OF RANDOM WALKS ON THE TRIANGULAR LATTICE129148ENSatoshiIshiwataHiroshiKawabiTsubasaTeruya10.18926/mjou/53045In the present paper, we study an explicit effect of non-symmetry on asymptotics of the n-step transition probability as n → ∞
for a class of non-symmetric random walks on the triangular lattice. Realizing the triangular lattice into R<sup>2</sup> appropriately, we observe that the
Euclidean distance in R<sup>2</sup> naturally appears in the asymptotics. We characterize this realization from a geometric view point of Kotani-Sunada’s
standard realization of crystal lattices. As a corollary of the main theorem, we obtain that the transition semigroup generated by the non-symmetric random walk approximates the heat semigroup generated by
the usual Brownian motion on R<sup>2</sup>.No potential conflict of interest relevant to this article was reported.