Consider a Brownian loop soup $\mathcal {L} _D^\theta $ with subcritical intensity $\theta\in
(0, 1/2] $ in some 2D bounded simply connected domain. We define and study the …

This article pertains to the classification of pairs of simple random curves with conformal
Markov property and symmetry. We give the complete classification of such curves …

The paper shows that the basis for termination of property relations in civil circulation can be
identified by the integrity of the legal system of a state. The author emphasises that right …

In this paper, we show that the interfaces in FK Ising model in any domain with 4 marked
boundary points and wired--free--wired--free boundary conditions conditioned on a specific …

Abstract A 2-SLE _ κ SLE κ (κ ∈ (0, 8) κ∈(0, 8)) is a pair of random curves (η _1, η _2)(η 1, η
2) in a simply connected domain D connecting two pairs of boundary points such that …

We show that if one conditions a cluster in a Brownian loop-soup L (of any intensity) in a two-
dimensional domain by a portion ∂ of its outer boundary, then in the remaining domain, the …

We prove that for κ∈(0, 8), if (η 1, η 2) is a 2-SLE κ pair in a simply connected domain D with
an analytic boundary point z 0, then as r→ 0+, P [dist (z 0, η j)< r, j= 1, 2] converges to a …

We consider the dimer model on piecewise Temperleyan, simply connected domains, on
families of graphs which include the square lattice as well as superposition graphs. We …

Schramm–Loewner evolution (SLE) curves describe the scaling limit of interfaces from many
2D lattice models. Heuristically speaking, the SLE partition function is the continuum …

We define intermediate SLE κ (ρ _) and reversed intermediate SLE κ (ρ _) processes using
Appell–Lauricella multiple hypergeometric functions, and use them to describe the time …