An exact solution of two friendly interacting directed walks near a sticky wall
R Tabbara, AL Owczarek, A Rechnitzer
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2014
We find the exact solution of two interacting friendly directed walks (modelling polymers) on the square lattice. These walks are confined to the quarter plane by a horizontal attractive surface, to capture the effects of DNA-denaturation and adsorption. We find the solution to the model's corresponding generating function by means of the obstinate kernel method. Specifically, we apply this technique in two different instances to establish partial solutions for two simplified generating functions of the same underlying model that ignore either surface or shared contacts. We then subsequently combine our two partial solutions to find the solution for the full generating function in terms of t..View full abstract
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Financial support from the Australian Research Council via its Discovery Projects scheme and the Centre of Excellence for Mathematics and Statistics of Complex Systems is gratefully acknowledged by the authors. One of the authors, RT, acknowledges financial support from the University of Melbourne via its Melbourne Research Scholarships scheme. Additionally, RT and ALO thank the Department of Mathematics, University of British Columbia, for hospitality. AR thanks the Department of Mathematics and Statistics, The University of Melbourne, for the office space and coffee.