2006, ISBN 0444527354, 279

The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer...

Random walks (Mathematics) | Mathematics | Stochastic processes

Random walks (Mathematics) | Mathematics | Stochastic processes

eBook

1993, Probability and its applications., ISBN 0817635890, xiv, 425

Book

2013, 1. Aufl., Modern Birkhauser classics, ISBN 1461460247, 435

The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple...

Self-avoiding walks (Mathematics) | Mathematics | Chemistry, Physical and theoretical | Statistical physics

Self-avoiding walks (Mathematics) | Mathematics | Chemistry, Physical and theoretical | Statistical physics

eBook

Probability Surveys, ISSN 1549-5787, 2007, Volume 4, Issue 1, pp. 1 - 79

Probability Surveys 2007, Vol. 4, 1-79 The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous...

Reinforced random walk | Urn model | Ṕolya's urn | VRRW | Dynamical system | Stochas-tic approximation | Self-avoiding walk | Agent-based model | Learning | Urn scheme | ERRW | Evo-lutionary game theory | Exchangeability | Lyapunov function | Mathematics - Probability

Reinforced random walk | Urn model | Ṕolya's urn | VRRW | Dynamical system | Stochas-tic approximation | Self-avoiding walk | Agent-based model | Learning | Urn scheme | ERRW | Evo-lutionary game theory | Exchangeability | Lyapunov function | Mathematics - Probability

Journal Article

The European Physical Journal B, ISSN 1434-6028, 9/2017, Volume 90, Issue 9, pp. 1 - 5

Using the Monte Carlo simulation, we investigate a memory-impaired self-avoiding walk on a square lattice in which a random walker marks each of sites visited...

Condensed Matter Physics | Solid State Physics | Physics, general | Fluid- and Aerodynamics | Complex Systems | Physics | PHYSICS, CONDENSED MATTER | SELF-AVOIDING WALK | MOTION | STOCHASTIC TRANSPORT | MODEL | Monte Carlo method | Alzheimer's disease

Condensed Matter Physics | Solid State Physics | Physics, general | Fluid- and Aerodynamics | Complex Systems | Physics | PHYSICS, CONDENSED MATTER | SELF-AVOIDING WALK | MOTION | STOCHASTIC TRANSPORT | MODEL | Monte Carlo method | Alzheimer's disease

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 12/2019, Volume 175, Issue 3, pp. 677 - 719

This article is concerned with self-avoiding walks (SAW) on $$\mathbb {Z}^{d}$$ Z d that are subject to a self-attraction. The attraction, which rewards...

Hammersley-Welsh argument | 82B27 | Statistics for Business, Management, Economics, Finance, Insurance | Self-attracting walk | Primary 60K35 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Linear polymers | Probability Theory and Stochastic Processes | Mathematics | Critical phenomena | Quantitative Finance | Self-avoiding walk | Operations Research/Decision Theory | Self-interacting random walk | Lace expansion | Secondary 60D05 | Attraction

Hammersley-Welsh argument | 82B27 | Statistics for Business, Management, Economics, Finance, Insurance | Self-attracting walk | Primary 60K35 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Linear polymers | Probability Theory and Stochastic Processes | Mathematics | Critical phenomena | Quantitative Finance | Self-avoiding walk | Operations Research/Decision Theory | Self-interacting random walk | Lace expansion | Secondary 60D05 | Attraction

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2017, Volume 50, Issue 26, p. 264003

We implement a scale-free version of the pivot algorithm and use it to sample pairs of three-dimensional self-avoiding walks, for the purpose of efficiently...

pivot algorithm | self-avoiding walk | Monte Carlo | critical exponent

pivot algorithm | self-avoiding walk | Monte Carlo | critical exponent

Journal Article

Discrete and Continuous Dynamical Systems - Series S, ISSN 1937-1632, 04/2017, Volume 10, Issue 2, pp. 289 - 311

We show that the 'erasing-larger-loops-first' (ELLF) method, which was first introduced for erasing loops from the simple random walk on the Sierpinski gasket,...

Loop-erased random walk | Fractal | Fractal dimension | Scaling limit | Sierpinski gasket | Displacement exponent | Self-avoiding walk | Self-repelling walk | MATHEMATICS, APPLIED | UNIFORM SPANNING-TREES | scaling limit | fractal dimension | fractal | PATHS | self-avoiding walk | displacement exponent | self-repelling walk

Loop-erased random walk | Fractal | Fractal dimension | Scaling limit | Sierpinski gasket | Displacement exponent | Self-avoiding walk | Self-repelling walk | MATHEMATICS, APPLIED | UNIFORM SPANNING-TREES | scaling limit | fractal dimension | fractal | PATHS | self-avoiding walk | displacement exponent | self-repelling walk

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 01/2019, Volume 475, Issue 2221, p. 20180549

The self-avoiding walk, and lattice spin systems such as the phi(4) model, are models of interest both in mathematics and in physics. Many of their important...

Critical exponent | Renormalization | model | Self-avoiding walk | LONG-RANGE | critical exponent | RIGOROUS CONTROL | MULTIDISCIPLINARY SCIENCES | SUSCEPTIBILITY | self-avoiding walk | O(N) MODELS | CRITICAL EXPONENTS | phi model | FIELD BEHAVIOR | renormalization | LOGARITHMIC CORRECTIONS | FINITE-RANGE DECOMPOSITION | CONVERGENCE | CRITICAL-BEHAVIOR | 1008 | φ4 model | 120

Critical exponent | Renormalization | model | Self-avoiding walk | LONG-RANGE | critical exponent | RIGOROUS CONTROL | MULTIDISCIPLINARY SCIENCES | SUSCEPTIBILITY | self-avoiding walk | O(N) MODELS | CRITICAL EXPONENTS | phi model | FIELD BEHAVIOR | renormalization | LOGARITHMIC CORRECTIONS | FINITE-RANGE DECOMPOSITION | CONVERGENCE | CRITICAL-BEHAVIOR | 1008 | φ4 model | 120

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2018, Volume 51, Issue 49, p. 490201

Journal Article

ANNALS OF PROBABILITY, ISSN 0091-1798, 09/2019, Volume 47, Issue 5, pp. 2801 - 2829

We study self-avoiding walk on graphs whose automorphism group has a transitive nonunimodular subgroup. We prove that self-avoiding walk is ballistic, that the...

transitive graph | nonunimodular | bubble diagram | PERCOLATION | STATISTICS & PROBABILITY | CONNECTIVE CONSTANTS | Self-avoiding walk | nonamenable | mean-field

transitive graph | nonunimodular | bubble diagram | PERCOLATION | STATISTICS & PROBABILITY | CONNECTIVE CONSTANTS | Self-avoiding walk | nonamenable | mean-field

Journal Article

2005, 1st ed., ISBN 044451709X, 368

With the mapping of the partition function graphs of the n-vector magnetic model in the n to 0 limit as the self-avoiding walks, the conformational statistics...

Self-avoiding walks (Mathematics) | Mathematical models | Polymers | Random walks (Mathematics) | Statistics | Agriculture & Farming

Self-avoiding walks (Mathematics) | Mathematical models | Polymers | Random walks (Mathematics) | Statistics | Agriculture & Farming

eBook

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 06/2019, Volume 524, pp. 362 - 374

In a signed network, nodes are connected by two types of logically contradictory links: positive and negative links. These two types of links may play...

Self-Avoiding Pruning Walk | Signed network model | Path length | Structural balance | PHYSICS, MULTIDISCIPLINARY | NETWORKS | GRAPHS | Electrical engineering | Analysis | Algorithms

Self-Avoiding Pruning Walk | Signed network model | Path length | Structural balance | PHYSICS, MULTIDISCIPLINARY | NETWORKS | GRAPHS | Electrical engineering | Analysis | Algorithms

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2019

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2018, Volume 51, Issue 20, p. 204001

We consider a simple cubic lattice self-avoiding walk model of 3-star polymers adsorbed at a surface and then desorbed by pulling with an externally applied...

self-avoiding walk | phase diagram | pulled adsorbing lattice star | CHAIN | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics

self-avoiding walk | phase diagram | pulled adsorbing lattice star | CHAIN | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 09/2019, Volume 946, p. 114696

Self-avoiding walks (SAWs) and loop-erased random walks (LERWs) are two ensembles of random paths with numerous applications in mathematics, statistical...

RENORMALIZATION-GROUP | 3-LOOP ORDER | SUPERSYMMETRY | SYMMETRY | CHARGE-DENSITY WAVES | DYNAMICS | SELF-AVOIDING WALK | FRACTAL DIMENSION | DISORDERED ELASTIC INTERFACES | CRITICAL EXPONENTS | PHYSICS, PARTICLES & FIELDS

RENORMALIZATION-GROUP | 3-LOOP ORDER | SUPERSYMMETRY | SYMMETRY | CHARGE-DENSITY WAVES | DYNAMICS | SELF-AVOIDING WALK | FRACTAL DIMENSION | DISORDERED ELASTIC INTERFACES | CRITICAL EXPONENTS | PHYSICS, PARTICLES & FIELDS

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 10/2012, Volume 154, Issue 1, pp. 149 - 163

We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed...

Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Local time | Trapping | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Self-interacting random walk | 60K37 | 60K99 | 60J55 | SELF-AVOIDING WALK | STATISTICS & PROBABILITY | REINFORCED RANDOM-WALK | Studies | Asymptotic methods | Random walk theory | Integers | Intervals | Asymptotic properties | Mathematical analysis | Lattices | Probability theory | Random walk | Mathematical models

Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Local time | Trapping | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Self-interacting random walk | 60K37 | 60K99 | 60J55 | SELF-AVOIDING WALK | STATISTICS & PROBABILITY | REINFORCED RANDOM-WALK | Studies | Asymptotic methods | Random walk theory | Integers | Intervals | Asymptotic properties | Mathematical analysis | Lattices | Probability theory | Random walk | Mathematical models

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 10/2015, Volume 48, Issue 45, pp. 454001 - 27

We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is...

compressive force | bridges | self-avoiding walks | Schramm-Loewner evolution | self-avoiding polygons | EXPONENTS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Functions (mathematics) | Half spaces | Mathematical analysis | Evolution | Boundaries | Compressed | Saws | Polygons

compressive force | bridges | self-avoiding walks | Schramm-Loewner evolution | self-avoiding polygons | EXPONENTS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Functions (mathematics) | Half spaces | Mathematical analysis | Evolution | Boundaries | Compressed | Saws | Polygons

Journal Article

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 10/2019, Volume 52, Issue 40, p. 405001

We consider self-avoiding walks terminally attached to a surface at which they can adsorb. A force is applied, normal to the surface, to desorb the walk and we...

POLYMER-CHAIN | phase diagram | pulled self-avoiding walks | adsorbing self-avoiding walks | Monte Carlo | PHYSICS, MULTIDISCIPLINARY | SURFACE | PHYSICS, MATHEMATICAL

POLYMER-CHAIN | phase diagram | pulled self-avoiding walks | adsorbing self-avoiding walks | Monte Carlo | PHYSICS, MULTIDISCIPLINARY | SURFACE | PHYSICS, MATHEMATICAL

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 4/2017, Volume 167, Issue 2, pp. 317 - 350

We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $$\mathbb {Z}^4$$ Z 4 , for sufficiently...

Collapse transition | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Renormalisation group | Weakly self-avoiding walk | Physics | Statistical Physics and Dynamical Systems | DIMENSIONS | FINITE-RANGE DECOMPOSITION | PHYSICS, MATHEMATICAL | LATTICE

Collapse transition | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Renormalisation group | Weakly self-avoiding walk | Physics | Statistical Physics and Dynamical Systems | DIMENSIONS | FINITE-RANGE DECOMPOSITION | PHYSICS, MATHEMATICAL | LATTICE

Journal Article

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