An expansion for self-interacting random walks

DOI10.1214/10-BJPS121zbMath1238.60116arXiv0706.0614MaRDI QIDQ654417

Remco van der Hofstad, Mark P. Holmes

Publication date: 28 December 2011

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.0614

zbMATH Keywords

law of large numberscentral limit theoremlace expansionrandom walk in random environmentself-interacting random walksexcited random walk, once-edge reinforced random walk

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Processes in random environments (60K37)

Related Items

Monotonicity for excited random walk in high dimensions ⋮ A monotonicity property for random walk in a partially random environment ⋮ A Monotonicity Property for Once Reinforced Biased Random Walk on $$\mathbb {Z}^d$$ ⋮ On the speed of once-reinforced biased random walk on trees ⋮ Random walks with local memory ⋮ Directed random graphs with given degree distributions ⋮ Self-attracting self-avoiding walk ⋮ Power Laws in Preferential Attachment Graphs and Stein's Method for the Negative Binomial Distribution ⋮ Loop-weighted walk

Cites Work

• Unnamed Item
• A monotonicity property for random walk in a partially random environment
• Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension: the higher-point functions
• Mean-field critical behaviour for percolation in high dimensions
• On the speed of a cookie random walk
• A survey of random processes with reinforcement
• The scaling limit of senile reinforced random walk.
• Convergence of lattice trees to super-Brownian motion above the critical dimension
• Self-avoiding walk in 5 or more dimensions
• The diffusion of self-avoiding random walk in high dimensions
• Phase transition in reinforced random walk and RWRE on trees
• The scaling limit of self-avoiding random walk in high dimensions
• The scaling limit of lattice trees in high dimensions
• Brownian motion and random walk perturbed at extrema
• Triangle condition for oriented percolation in high dimensions
• A new inductive approach to the lace expansion for self-avoiding walks
• The scaling limit of the incipient infinite cluster in high-dimensional percolation. I: Critical exponents
• Gaussian limit for critical oriented percolation in high dimensions.
• A generalised inductive approach to the lace expansion
• Once edge-reinforced random walk on a tree
• Gaussian scaling for the critical spread-out contact process above the upper critical dimension
• Excited random walk
• Convergence of critical oriented percolation to super-Brownian motion above \(4+1\) dimensions
• Cut points and diffusive random walks in random environment
• Monotonicity for excited random walk in high dimensions
• Recurrence and transience of excited random walks on \(\mathbb Z^d\) and strips
• Central limit theorem for the excited random walk in dimension \(d\geq 2\)
• Multi-excited random walks on integers
• On the upper critical dimension of lattice trees and lattice animals
• The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion
• Analysis and Stochastics of Growth Processes and Interface Models
• Convergence of self-avoiding random walk to Brownian motion in high dimensions
• THE LACE EXPANSION FOR SELF-AVOIDING WALK IN FIVE OR MORE DIMENSIONS
• Lattice trees and super-Brownian motion
• The excited random walk in one dimension
• The lace expansion approach to ballistic behaviour for one-dimensional weakly self-avoiding walks

This page was built for publication: An expansion for self-interacting random walks