E W James and C E Soteros 2007 J. Phys. A: Math. Theor. 40 8621 doi:10.1088/1751-8113/40/30/002
New pattern theorems for square lattice self-avoiding walks and self-avoiding polygons
E W James1 and C E Soteros2
Show affiliationsA general pattern theorem for weighted self-avoiding polygons (SAPs) and self-avoiding walks (SAWs) in 
is obtained. The pattern theorem for SAPs fits into the general framework of the pattern theorem for lattice clusters introduced by Madras (1999 Ann. Comb. 3 357–84). Note that, unlike other pattern theorems proved for SAPs, this pattern theorem does not rely on first establishing a relationship between SAPs and SAWs. These results are applied to obtain pattern theorems for self-interacting SAPs and self-interacting SAWs.
- PACS
- MSC
-
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
-
Issue 30 (27 July 2007)
Received 12 March 2007, in final form 11 June 2007
Published 12 July 2007
-
New pattern theorems for square lattice self-avoiding walks and self-avoiding polygons
E W James and C E Soteros 2007 J. Phys. A: Math. Theor. 40 8621
-
Higher order Morita approximations for random copolymer adsorption
J Alvarez et al 2007 J. Phys. A: Math. Theor. 40 F289
-
The statistics of collapsing square lattice trails with a fixed number of vertices of degree 4
E W James and C E Soteros 2007 J. Phys. A: Math. Theor. 40 14945
-
Self-avoiding polygons and walks in slits
J Alvarez et al 2008 J. Phys. A: Math. Theor. 41 185004
-
Localization of a random copolymer at an interface: an exact enumeration study
E W James et al 2003 J. Phys. A: Math. Gen. 36 11575
-
Localization of a random copolymer at an interface: an untethered self-avoiding walk model
E W James et al 2003 J. Phys. A: Math. Gen. 36 11187
-
The statistical mechanics of random copolymers
C E Soteros and S G Whittington 2004 J. Phys. A: Math. Gen. 37 R279
-
Eulerian graph embeddings and trails confined to lattice tubes
C E Soteros 2006 J. Phys.: Conf. Ser. 42 258
-
Detecting cavities by electrostatic boundary measurements
Giovanni Alessandrini et al 2002 Inverse Problems 18 1333
-
A simple parameter-free wavefunction for the ground state of two-electron atoms
L U Ancarani et al 2007 J. Phys. B: At. Mol. Opt. Phys. 40 2695
Related review articles
What's this?- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain
- Discrete breathers and the anomalous decay of luminescence