Related papers: Two-curve Green's function for $2$-SLE: the interi…

We consider long-range percolation, Ising model, and self-avoiding walk on $\mathbb{Z}^d$, with couplings decaying like $|x|^{-(d+\alpha)}$ where $0 < \alpha \le 2$, above the upper critical dimensions. In the spread-out setting where the…

We study the adjacency graph of bubbles---i.e., complementary connected components---of an SLE$_{\kappa}$ curve for $\kappa \in (4,8)$, with two such bubbles considered to be adjacent if their boundaries intersect. We show that this…

In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the…

In this article, we give an explicit relationship of SLE partition functions with Coulomb gas formalism of conformal field theory. We first construct a family of SLE$(\kappa)$ partition functions as Coulomb gas integrals and derive their…

In this paper, we show how the two-particle Green function (2PGF) can be obtained within the framework of the Dual Fermion approach. This facilitates the calculation of the susceptibility in strongly correlated systems where long-ranged…

We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm's SLE curves with parameter $\kappa=3$ and $\kappa=16/3$…

Recently, an exact Green's function of the diffusion equation for a pair of spherical interacting particles in two dimensions subject to a backreaction boundary condition was derived. Here, we use the obtained Green's function to calculate…

We provide explicit formulas for the Green function of an elliptic PDE in the infinite strip and the half-plane. They are expressed in elementary and special functions. Proofs of uniqueness and existence are also given.

Using results established in other papers in our series, we prove the existence of the infinite volume, temperature zero, thermodynamic Green's functions of a two dimensional, weakly coupled fermion gas with an asymmetric Fermi curve and…

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p variation, 1\leq…

We derive a surprising correspondence between SLE$_{\kappa}(\rho)$ processes and light cones of the Gaussian free field (GFF). Recall that (one-sided, chordal, origin-seeded) SLE$_\kappa(\rho)$ processes are in some sense the simplest and…

We consider collections of $N$ chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain. We define and study candidates for such limits in…

Various features of the two-parameter family of Schramm-Loewner evolutions SLE(\kappa,\rho) are studied. In particular, we derive certain restriction properties that lead to a ``strong duality'' conjecture, which is an identity in law…

The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…

Let $\gamma$ be the curve generating a Schramm--Loewner Evolution (SLE) process, with parameter $\kappa\geq0$. We prove that, with probability one, the Hausdorff dimension of $\gamma$ is equal to $\operatorname {Min}(2,1+\kappa/8)$.

We consider a one-dimensional gas of spin-1/2 fermions interacting through $\delta$-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point…

We compute the almost-sure Hausdorff dimension of the double points of chordal SLE_kappa for kappa > 4, confirming a prediction of Duplantier-Saleur (1989) for the contours of the FK model. We also compute the dimension of the cut points of…

We give a simplified and complete proof of the convergence of the chordal exploration process in critical FK-Ising percolation to chordal SLE$_\kappa( \kappa-6)$ with $\kappa=16/3$. Our proof follows the classical excursion-construction of…

We study the topology of two-dimensional open systems in terms of the Green's function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems, which indicates the number difference of gapless edge…

Let $K\subset \mathbb R$ be a regular compact set and let $g(z)=g_{\overline{\mathbb C}\setminus K}(z,\infty)$ be the Green function for $\overline{\mathbb C}\setminus K$ with pole at infinity. For $\delta>0$, define $$ G(\delta):=\max\{…