Abstract
The author considers directed percolation on the square lattice, with probability pH(pV) for the horizontal (vertical) bonds to be unbroken. For pH=1- epsilon ( epsilon small) and pV> sigma ( epsilon ) the percolating cluster is asymptotically within a cone phi +< phi < phi +. The author calculates phi +or- and the fluctuations of the boundaries at phi = phi +or- as power series in epsilon , up to terms approximately epsilon 2, showing that the transverse spread of the percolating cluster is random walk-like. For any given pH the percolation threshold pV,c( epsilon ), defined by phi += phi - at pV=pV,c is also calculated.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
