Adsorbing staircase walks and staircase polygons
Copyright policy )Adsorbing staircase walks and staircase polygons
The author finds generating functions of adsorbing random staircase walks and staircase polygons on the main diagonal of the square lattice, using the algebraic languages of Dyck and Motzkin [cf. \textit{M.-P. Delest} and \textit{G. X. Viennot}, Theor. Comput. Sci. 34, No. 1-2, 169-206 (1984)] and partial difference equations, proposed by \textit{R. Brak}, \textit{J. W. Essam} and \textit{A. L. Owczarek} [J. Stat. Phys. 93, No. 1-2, 155-192 (1998)]. The adsorption transition is evaluated by means of the associated critical exponent.
- York University Canada
Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics, adsorbing random staircase walks, adsorption transition, generating functions, Exact enumeration problems, generating functions, staircase polygons, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Exactly solvable models; Bethe ansatz
Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics, adsorbing random staircase walks, adsorption transition, generating functions, Exact enumeration problems, generating functions, staircase polygons, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Exactly solvable models; Bethe ansatz
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