Related papers: SLE and the free field: Partition functions and co…
We implement a version of conformal field theory (CFT) that gives a connection to SLE in a multiply connected domain. Our approach is based on the Gaussian free field and applies to CFTs with central charge $c \leq 1$. In this framework we…
The square lattice is perhaps the simplest cellular structure. In this work, however, we investigate the various structural and topological properties of the kinetic and stochastic counterpart of the square lattice and termed them as…
A quantum surface (QS) is an equivalence class of pairs $(D,H)$ of simply connected domains $D\subsetneq\mathbb{C}$ and random distributions $H$ on $D$ induced by the conformal equivalence for random metric spaces. This distribution-valued…
Extending the Schramm--Loewner Evolution (SLE) to model branching structures while preserving conformal invariance and other stochastic properties remains a formidable research challenge. Unlike simple paths, branching structures, or trees,…
We review some recently completed research that establishes the scaling limit of Fomin's identity for loop-erased random walk on Z^2 in terms of the chordal Schramm-Loewner evolution (SLE) with parameter 2. In the case of two paths, we…
We consider the boundary WZW model on a half-plane with a cut growing according to the Schramm-Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and at infinity. We study necessary and sufficient conditions…
We study the relationship between certain SLE$_\kappa(\rho)$ processes, which are variants of the Schramm-Loewner evolution with parameter $\kappa$ in which one keeps track of an extra marked point, and Liouville quantum gravity (LQG).…
We study the interaction of a scalar and a spinning particle with a coherent linearized gravitational wave field treated as a classical spin two external field. The spin degrees of freedom of the spinning particle are described by…
Domain walls for spin glasses are believed to be scale invariant invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to…
We discuss the sigma model on the $PSL(n|n)$ supergroup manifold. We demonstrate that this theory is exactly conformal. The chiral algebra of this model is given by some extension of the Virasoro algebra, similar to the $W$ algebra of…
It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Loewner evolutions. Based on the existence of a logarithmic null vector in an indecomposable…
We study functional stochastic differential equations with a locally unbounded, functional drift focusing on well-posedness, stability and the strong Feller property. Following the non-functional case, we only consider integrability…
The massive harmonic explorer is a model of random discrete path on the hexagonal lattice that was proposed by Makarov and Smirnov as a massive perturbation of the harmonic explorer. They argued that the scaling limit of the massive…
Let $D={\mathbb H}\setminus \bigcup_{j=1}^N C_j$ be a standard slit domain, where ${\mathbb H}$ is the upper half plane and $C_j,1\le j\le N,$ are mutually disjoint horizontal line segments in ${\mathbb H}$. A stochastic Komatu-Loewner…
We prove that the scaling limit of loop-erased random walk in a simply connected domain $D$ is equal to the radial SLE(2) path in $D$. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the…
We study the quantization problem of relativistic scalar and spinning particles interacting with a radiation electromagnetic field by using the path integral and the external source method. The spin degrees of freedom are described in terms…
We define a minimization problem for paths on planar graphs that, on the honeycomb lattice, is equivalent to the exploration path of the critical site percolation and than has the same scaling limit of SLE_6. We numerically study this model…
Stochastic differential equations (SDEs) without global Lipschitz drift often demonstrate unusual phenomena. In this paper, we consider the following SDE on $\mathbb R^d$: \begin{align*} \mathrm{d} \mathbf{X}_t=\mathbf{b}(\mathbf{X}_t)…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Sheffield showed that conformally welding a $\gamma$-Liouville quantum gravity (LQG) surface to itself gives a Schramm-Loewner evolution (SLE) curve with parameter $\kappa = \gamma^2$ as the interface, and Duplantier-Miller-Sheffield proved…