Related papers: Near-critical dimers and massive SLE
The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
We show that the N=8 superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed N=6 superconformal U(N)xU(N) Chern-Simons-matter theories at level (k,…
Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced…
A new set of infinitesimal transformations generalizing scale invariance for strongly anisotropic critical systems is considered. It is shown that such a generalization is possible if the anisotropy exponent \theta =2/N, with N=1,2,3 ...…
We construct an application, which takes as input a simple path and a possibly infinite collection of loops, and outputs a continuous path by adding the loops chronologically to the simple path as the simple path encounters them. By…
This is the first article in a series of two papers in which we study the Temperleyan dimer model on an arbitrary bounded Riemann surface of finite topolgical type. The end goal of both papers is to prove the convergence of height…
In this paper we consider uniformly random lozenge tilings of arbitrary domains approximating (after suitable normalization) a closed, simply-connected subset of $\mathbb{R}^2$ with piecewise smooth, simple boundary. We show that the local…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
Recently the existence of a random critical line in two dimensional Dirac fermions is confirmed. In this paper, we focus on its scaling properties, especially in the critical region. We treat Dirac fermions in two dimensions with two types…
The N\'eel temperature, staggered magnetization density, as well as the spinwave velocity of a three-dimensional (3D) quantum Heisenberg model with antiferromagnetic disorder (randomness) are calculated using first principles…
We consider uniform spanning tree (UST) in topological polygons with $2N$ marked points on the boundary with alternating boundary conditions. In [LPW21], the authors derive the scaling limit of the Peano curve in the UST. They are variants…
We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…
Schramm Loewner Evolution (SLE) is a one-parameter family of random planar curves introduced by Oded Schramm in 1999 as the candidates for the scaling limits of the interfaces in the planar critical lattice models. This is the only possible…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
We consider a 2-dimensional model of random walk in random environment known as line model. The environment is described by two independent families of i.i.d. random variables dictating rates of jumps in vertical, respectively horizontal…
Motivated by applications, the last few years have witnessed tremendous interest in understanding the structure as well as the behavior of dynamics for inhomogeneous random graph models. In this study we analyze the maximal components at…
Nonlinear sigma models with non-compact target space and non-amen-able symmetry group were introduced long ago in the study of disordered electron systems. They also occur in dimensionally reduced quantum gravity; recently they have been…
We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centers. At a dynamical level, the hidden…