Related papers: Whole-plane self-avoiding walks and radial Schramm…

We consider a model of planar random aggregation from the ALE$(0,\eta)$ family where particles are attached preferentially in areas of low harmonic measure. We find that the model undergoes a phase transition in negative $\eta$, where for…

The Brownian excursion measure is a conformally invariant infinite measure on curves. It figured prominently in one of the first major applications of SLE, namely the explicit calculations of the planar Brownian intersection exponents from…

This paper introduces the annulus SLE$_\kappa$ processes in doubly connected domains. Annulus SLE$_6$ has the same law as stopped radial SLE$_6$, up to a time-change. For $\kappa\not=6$, some weak equivalence relation exists between annulus…

In quantum mechanics, the Schrieffer--Wolff (SW) transformation (also called quasi-degenerate perturbation theory) is known as an approximative method to reduce the dimension of the Hamiltonian. We present a geometric interpretation of the…

Stochastic Loewner Evolution (SLE_kappa) has been introduced as a description of the continuum limit of cluster boundaries in two-dimensional critical systems. We show that the problem of N radial SLEs in the unit disc is equivalent to…

We consider evolution in the unit disk in which the sample paths are represented by the trajectories of points evolving randomly under the generalized Loewner equation. The driving mechanism differs from the SLE evolution, but nevertheless…

We derive a rate of convergence of the Loewner driving function for planar loop-erased random walk to Brownian motion with speed 2 on the unit circle, the Loewner driving function for radial SLE(2). The proof uses a new estimate of the…

Schramm--Loewner evolution (SLE) has been one of the central topics in the probabilistic study of two-dimensional critical systems. It is a random curve in two dimensions to which a cluster interface in a critical lattice system is…

We disclose the origin of anisotropic percolation perimeters in terms of the Stochastic Loewner Evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multi-layered and directed…

Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process, also has an appropriately defined bridge…

We demonstrate how to obtain integrable results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville quantum gravity (LQG). In particular, we prove an exact…

We reduce the problem of counting self-avoiding walks in the square lattice to a problem of counting the number of integral points in multidimensional domains. We obtain an asymptotic estimate of the number of self-avoiding walks of length…

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponents $\nu$ and $2\Delta_4…

Avalanche frontiers in Abelian Sandpile Model (ASM) are random simple curves whose continuum limit is known to be a Schramm-Loewner Evolution (SLE) with diffusivity parameter $\kappa = 2$. In this paper we consider the dissipative ASM and…

We derive the exact value of intersection exponents between planar Brownian motions or random walks, confirming predictions from theoretical physics by Duplantier and Kwon. Let B and B' be independent Brownian motions (or simple random…

We find statistical evidence for a mismatch between the (global) spatial curvature parameter $K$ in the geodesic equation for incoming photons, and the corresponding parameter in the Friedmann equation that determines the time evolution of…

We consider a self-avoiding walk model (SAW) on the faces of the square lattice $\mathbb{Z}^2$. This walk can traverse the same face twice, but crosses any edge at most once. The weight of a walk is a product of local weights: each square…

It has been recently argued that interacting self-avoiding walks (ISAW) of length $ \ell , $ in their low temperature phase (i.e. below the $ \Theta $-point) should have a partition function of the form: $$ Q_{\ell} \sim \mu^{ \ell}_ 0\mu^{…

We study self-avoiding walks on the square lattice restricted to a square box of side $L$ weighted by a length fugacity without restriction of their end points. This models a confined polymer in dilute solution. The model admits a phase…

Using results from Schramm Loewner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various 2-dimensional domain geometries. We generalize to two polymers and…