Related papers: On Self-Avoiding Walks across n-Dimensional Dice a…
We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling…
The statistics of a long closed self-avoiding walk (SAW) or polymer ring on a $ d $-dimensional lattice obeys hyperscaling. The combination $ p_N \left\langle R^2 \right\rangle^{ d/2}_N\mu^{ -N}, $ (where $ p_N $ is the number of…
We introduce SamBa-GQW, a novel quantum algorithm for solving binary combinatorial optimization problems of arbitrary degree with no use of any classical optimizer. The algorithm is based on a continuous-time quantum walk on the solution…
We consider the phase diagram of self-avoiding walks (SAW) on the simple cubic lattice subject to surface and bulk interactions, modeling an adsorbing surface and variable solvent quality for a polymer in dilute solution, respectively. We…
We describe a new algebraic technique for enumerating self-avoiding walks on the rectangular lattice. The computational complexity of enumerating walks of $N$ steps is of order $3^{N/4}$ times a polynomial in $N$, and so the approach is…
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…
Self-attracting walks (SATW) with attractive interaction u > 0 display a swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >= 2, analogous to the \Theta transition of polymers. We are interested in the structure of…
We perform a Monte Carlo simulation of two-dimensional N-step interacting self-avoiding walks at the theta point, with lengths up to N=3200. We compute the critical exponents, verifying the Coulomb-gas predictions, the theta-point…
We study an annealed model of Uniform Infinite Planar Quadrangulation (UIPQ) with an infinite two-sided self-avoiding walk (SAW), which can also be described as the result of glueing together two independent uniform infinite…
For $d \geq 2$ and $n \in \mathbb{N}$, let $\mathsf{W}_n$ denote the uniform law on self-avoiding walks of length $n$ beginning at the origin in the nearest-neighbour integer lattice $\mathbb{Z}^d$, and write $\Gamma$ for a…
The pivot algorithm -- we also call it the pivot chain -- is an algorithm for approximately uniform sampling from $\Omega _{N},$ the set of $N$-step self-avoiding walks on $\mathbb{Z}^{d}$ ($N,$ $d\geq 1$). Based on this algorithm and the…
The scaling behavior of self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by Monte Carlo simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our…
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…
Mesh representation by random walks has been shown to benefit deep learning. Randomness is indeed a powerful concept. However, it comes with a price: some walks might wander around non-characteristic regions of the mesh, which might be…
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…
A growing self-avoiding walk (GSAW) is a stochastic process that starts from the origin on a lattice and grows by occupying an unoccupied adjacent lattice site at random. A sufficiently long GSAW will reach a state in which all adjacent…
We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
We study the connective constants of weighted self-avoiding walks (SAWs) on infinite graphs and groups. The main focus is upon weighted SAWs on finitely generated, virtually indicable groups. Such groups possess so-called 'height…
We study the problem of counting all cycles or self-avoiding walks (SAWs) on triangulated planar graphs. We present a subexponential $2^{O(\sqrt{n})}$ time algorithm for this counting problem. Among the technical ingredients used in this…