The dilute A L models and the integrable perturbations of unitary minimal CFTs. Abstract Recently, a set of thermodynamic Bethe ansatz equations is proposed by Dorey, Pocklington and Tateo for unitary minimal models perturbed by φ 1,2 or φ 2,1 operator. We examine their results in view of the lattice analogues, dilute A L models at regime 1 and 2. Taking M 5,6 + φ 1,2 and M 3,4 + φ 2,1 as the s...

We consider the double scaling limit in the random matrix ensemble with an external source 1 Zn e−nTr( 1 2 M −AM)d M defined on n×n Hermitian matrices, where A is a diagonal matrix with two eigenvalues ±a of equal multiplicities. The value a = 1 is critical since the eigenvalues of M accumulate as n → ∞ on two intervals for a > 1 and on one interval for 0 < a < 1. These two cases were treated i...

We consider two species of particles performing random walks in a domain in R with reflecting boundary conditions, which annihilate on contact. In addition there is a conservation law so that the total number of particles of each type is preserved: When the two particles of different species annihilate each other, particles of each species, chosen at random, give birth. We assume initially equa...

The system of semi-relativistic particles coupled to a scalar bose field is investigated. A renormalized Hamiltonian is defined by subtracting a divergent term from the total Hamiltonian. We consider taking the scaling limit and removing the ultraviolet cutoffs simultaneously for the renormalized Hamiltonian. By applying an abstract scaling limit theory on self-adjoint operators, we derive the ...

We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we will consider the convergence of critical crossing probabilities to Cardy’s formula and of the critical exploration path to chordal SLE6, the full scaling limit of critical cluster boundaries, and near-critical scaling limits.

Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while the latter quantifies their tendency to form logarithmic spirals. We show how these characteristics are related to local operators of conformal field theory a...

The canonical application of multidimensional scaling (MDS) methods has been to color dissimilarities, visualizing these as distances in a low-dimensional space. Some questions remain: How well can the locations of stimuli in color space be recovered when data are sparse, and how well can systematic individual variations in perceptual scaling be distinguished from stochastic noise? We collected...

We study the Laplacian-∞ path as an extreme case of the Laplacian-α random walk. Although, in the finite α case, there is reason to believe that the process converges to SLEκ, with κ = 6/(2α+ 1), we show that this is not the case when α = ∞. In fact, the scaling limit depends heavily on the lattice structure, and is not conformal (or even rotational) invariant.

We construct a Hamiltonian which in a scaling limit becomes equivalent to one that can be diagonalized by a Bogoliubov transformation. There may appear simultaneously a mean-field and a superconducting phase. They influence each other in a complicated way. For instance, an attractive mean field may stimulate the superconducting phase and a repulsive one may destroy it.

We consider two species of particles performing random walks in a domain in R with reflecting boundary conditions, which annihilate on contact. In addition there is a conservation law so that the total number of particles of each type is preserved: When the two particles of different species annihilate each other, particles of each species, chosen at random, give birth. We assume initially equa...