hp home products & services support solutions how to buy
hp logo - invent
corner hp labs corner
search search
contact hp contact hp
hp labs home hp labs home
about hp labs about hp labs
research research
news and events news and events
careers @ labs careers @ labs
technical reports technical reports
talks and speeches talks and speeches
worldwide sites worldwide sites
corner corner
HP Labs Technical Reports

Click here for full text: Postscript PDF

The Critical Attractive Random Polymer in Dimension One

van der Hofstad, Remco; Klenke, Achim; Konig, Wolfgang


Keyword(s): one-dimensional polymers; repulsive and attractive interaction; phase transition; local times of simple random walk

Abstract: Please Note. This abstract contains mathematical formulae which cannot be represented here. A polymer chain with attractive and repulsive forces between the monomers is modeled by attaching a weight e-* for every self-intersection and e /(2d) for every self-contact to the probability of an n-stepsimple random walk on Z d , where *, > 0 are parameters. It is known that for d =1 and > * the chain collapses down to finitely many sites, while for d =1 and <* it spreads out ballistically. Here we study for d = 1 the critical case =* and show that the end- to-end distance runs on the scale n = (log n) -1/4 . We describe the asymptotic shape of the accordingly scaled local times in terms of an explicit variational formula and prove that the scaled polymer chain occupies a region of size n times a constant. Moreover, we derive the asymptotics of the partition function. Notes: Remco van der Hofstad, Department of Applied Mathematics, Delft University of Technology, 2628 CD Delft, The Netherlands. Achim Klenke, Department of Mathematics, Erlangen-Nurnberg University, Bismarckstrae 1 , 91054 Erlangen, Germany

30 Pages

Back to Index

printing icon
printing instructions printing instructions
Privacy Statement Legal Notices © 1994-2000 Hewlett-Packard Company