Domino Tilings with One Diagonal Impurity

• Autorzy: Nakano F. , Sadahiro T.
• Języki publikacji: EN

Abstrakty

EN

This paper studies the dimer model on the dual graph of the square-octagon lattice, which can be viewed as the domino tilings with impurities in some sense. In particular, under a certain boundary condition where only one impurity is contained, we give an exact formula representing the probability of finding an impurity at a given site in a uniformly random dimer configuration in terms of simple random walks on the square lattice.

Słowa kluczowe

EN

dimer model; domino tilings

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 117, nr 1-4
• Strony: 249--264
• Opis fizyczny: Bibliogr. 8 poz., rys., wykr.

Twórcy

autor

Nakano F.

autor

Sadahiro T.

• Department of Computer Science, Tsuda College Tokyo 187-8577, Japan,

Bibliografia

• [1] N. Biggs. Algebraic Graph Theory. Cambridge University Press, 1994.
• [2] R. Burton and R. Pemantle. Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances. Annals of Probability, 21:1329-1371, 1993.
• [3] H. Cohn R. Kenyon and J. Propp. A variational principle for domino tilings. J. Amer. Math. Soc., 14:297-3462, 2001.
• [4] R. Kenyon A. Okounkov and S. Sheffield. Dimers and amoebae. Ann. Math., 163 no. 3:1019-1056, 2006.
• [5] R. Kenyon J. Propp and D. Wilson. Trees and matchings. Electronic Journal of Combinatorics, 7:#R25, 2000.
• [6] F. Nakano, H. Ono and T. Sadahiro. Local move connectedness of domino tilings with diagonal impurities. Discrete Mathematics, 310 1918-1931, 2010.
• [7] F. Nakano and T. Sadahiro. A Bijection Theorem for Domino Tilings with Diagonal Impurities. Journal of Statistical Physics, Volume 139, Number 4, 565-597, 2010.
• [8] R. Pemantle. Choosing a spanning tree for the integer lattice uniformly. Annals of Probability, 19:1559 - 1574, 1991.