相关论文: Scaling of Self-Avoiding Walks and Self-Avoiding T…

This paper analyzes a random walk model for the level lines appearing in the entropic repulsion phenomena of three-dimensional discrete random interfaces above a hard wall; we are particularly motivated by the low-temperature (2+1)D…

We study the critical behavior of surface-interacting self-avoiding random walks on a class of truncated simplex lattices, which can be labeled by an integer $n\ge 3$. Using the exact renormalization group method we have been able to obtain…

We investigate polymers pulled away from an interacting surface, where the force is applied to the untethered endpoint and at an angle $\theta$ to the surface. We use the canonical self-avoiding walk model of polymers and obtain the phase…

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in…

We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in…

Results of a numerically exact transfer matrix calculation for the model of Interacting Self-Avoiding Trails are presented. The results lead to the conclusion that, at the collapse transition, Self-Avoiding Trails are in the same…

We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on…

Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" (TSAW) model of Amit, Parisi, and Peliti in two dimensions. The walks in it…

We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when…

Kinetically grown self-avoiding walks on various types of generalized random networks have been studied. Networks with short- and long-tailed degree distributions $P(k)$ were considered ($k$, degree or connectivity), including scale-free…

We consider self-avoiding walks (SAWs) on the backbone of percolation clusters in space dimensions d=2, 3, 4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the…

Long-distance characteristics of small-world networks have been studied by means of self-avoiding walks (SAW's). We consider networks generated by rewiring links in one- and two-dimensional regular lattices. The number of SAW's $u_n$ was…

We have analysed the recently extended series for the number of self-avoiding walks (SAWs) $C_L(1)$ that cross an $L \times L$ square between diagonally opposed corners. The number of such walks is known to grow as $\lambda_S^{L^2}.$ We…

A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $\nu$ and $\chi$ are calculated for various different occupation probabilities,…

In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…

We define a new ensemble for self-avoiding walks in the upper half-plane, the fixed irredicible bridge ensemble, by considering self-avoiding walks in the upper half-plane up to their $n$-th bridge height, $Y_n$, and scaling the walk by…

We consider a long-range version of self-avoiding walk in dimension $d > 2(\alpha \wedge 2)$, where $d$ denotes dimension and $\alpha$ the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to…

The smart kinetic self-avoiding walk (SKSAW) is a random walk which never intersects itself and grows forever when run in the full-plane. At each time step the walk chooses the next step uniformly from among the allowable nearest neighbors…

Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by Nienhuis that the connective constant of self-avoiding walks on the honeycomb lattice is $\sqrt{2+\sqrt{2}}.$ A key identity used in that proof depends on the…

It was discovered a few years ago that many networks in the real world exhibit self-similarity. A lot of researches on the structures and processes on real and artificial fractal complex networks have been done, drawing an analogy to…