[图书][B] Complexity: knots, colourings and counting
DJA Welsh - 1993 - books.google.com
These notes are based on a series of lectures given at the Advanced Research Institute of
Discrete Applied Mathematics held at Rutgers University. Their aim is to link together …
Discrete Applied Mathematics held at Rutgers University. Their aim is to link together …
Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory
We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and
prove some rigorous theorems on the regularity properties and possible pathologies of the …
prove some rigorous theorems on the regularity properties and possible pathologies of the …
[图书][B] Random walks, critical phenomena, and triviality in quantum field theory
Simple random walks-or equivalently, sums of independent random vari ables-have long
been a standard topic of probability theory and mathemat ical physics. In the 1950s, non …
been a standard topic of probability theory and mathemat ical physics. In the 1950s, non …
Self-avoiding walk in five or more dimensions I. The critical behaviour
We use the lace expansion to study the standard self-avoiding walk in the d-dimensional
hypercubic lattice, for d≧ 5. We prove that the number cn of n-step self-avoiding walks …
hypercubic lattice, for d≧ 5. We prove that the number cn of n-step self-avoiding walks …
Monte Carlo methods for the self-avoiding walk
EJJ Van Rensburg - Journal of Physics A: Mathematical and …, 2009 - iopscience.iop.org
The numerical simulation of self-avoiding walks remains a significant component in the
study of random objects in lattices. In this review, I give a comprehensive overview of the …
study of random objects in lattices. In this review, I give a comprehensive overview of the …
[图书][B] The statistical mechanics of interacting walks, polygons, animals and vesicles
EJJ Van Rensburg - 2015 - books.google.com
The self-avoiding walk is a classical model in statistical mechanics, probability theory and
mathematical physics. It is also a simple model of polymer entropy which is useful in …
mathematical physics. It is also a simple model of polymer entropy which is useful in …
[图书][B] The Lace Expansion and Its Applications: Ecole D'Eté de Probabilités de Saint-Flour XXXIV-2004
G Slade - 2006 - Springer
We consider independent Bernoulli bond percolation on the integer lattice Zd, with edge
(bond) set consisting of pairs {x, y} of vertices of Zd with y− x∈ Ω, where Ω defines either the …
(bond) set consisting of pairs {x, y} of vertices of Zd with y− x∈ Ω, where Ω defines either the …
Tree-based models for random distribution of mass
D Aldous - Journal of Statistical Physics, 1993 - Springer
A mathematical model for distribution of mass in d-dimensional space, based upon
randomly embedding random trees into space, is introduced and studied. The model is a …
randomly embedding random trees into space, is introduced and studied. The model is a …
Self-avoiding walk is sub-ballistic
H Duminil-Copin, A Hammond - Communications in Mathematical Physics, 2013 - Springer
We prove that self-avoiding walk on Z^ d Z d is sub-ballistic in any dimension d≥ 2. That is,
writing ‖ u ‖‖ u‖ for the Euclidean norm of u ∈ Z^ du∈ Z d, and P_ SAW _n P SAW n for …
writing ‖ u ‖‖ u‖ for the Euclidean norm of u ∈ Z^ du∈ Z d, and P_ SAW _n P SAW n for …
Self-avoiding-walk contacts and random-walk self-intersections in variable dimensionality
JF Douglas, T Ishinabe - Physical Review E, 1995 - APS
The average number of nearest-neighbor (NN) contacts< m> of self-avoiding walks (SAW's)
on a hypercubic lattice is calculated using direct enumeration and 1/d expansion methods …
on a hypercubic lattice is calculated using direct enumeration and 1/d expansion methods …