Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 AN EXPLICIT EFFECT OF NON-SYMMETRY OF RANDOM WALKS ON THE TRIANGULAR LATTICE 129 148 EN Satoshi Ishiwata Hiroshi Kawabi Tsubasa Teruya 10.18926/mjou/53045 In 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 R² appropriately, we observe that the Euclidean distance in R² 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 R². No potential conflict of interest relevant to this article was reported.