In probability theory, the Schramm–Loewner evolution with parameter κ, also known as stochastic Loewner evolution (SLEκ), is a family of random planar...

of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory. Schramm was born in Jerusalem...

dimensions of random walks, where the random walks are defined via Schramm–Loewner evolution (SLE). As we have seen above, CFTs describe the physics of phase...

processes such as self-avoiding random walks, Brownian motion, Schramm–Loewner evolution, and related theories in probability theory and mathematical physics...

and probability theory, including Teichmüller theory, the Schramm–Loewner evolution, and Loewner energy. Originally from China, and educated in France and...

stochastic processes, including graphons, random planar maps, the Schramm–Loewner evolution, and their applications to quantum gravity. She was a Junior Fellow...

processes and even potential theory. It is the driving process of Schramm–Loewner evolution. In applied mathematics, the Wiener process is used to represent...

mathematics, the Loewner differential equation, or Loewner equation, is an ordinary differential equation discovered by Charles Loewner in 1923 in complex...

the conjecture of Oded Schramm that the scaling limit of a large cluster may be described in terms of a Schramm–Loewner evolution. This conjecture was proved...

function (mathematics) Quantum probability Percolation theory Schramm–Loewner evolution List of textbooks in thermodynamics and statistical mechanics...

probability theory and best known for his work since 2000 on the Schramm–Loewner evolution. He received his PhD from Princeton University in 1979 under the...

process Poisson process Compound Non-homogeneous Quasimartingale Schramm–Loewner evolution Semimartingale Sigma-martingale Stable process Superprocess Telegraph...

Sarpy County, Nebraska, U.S. 113952 Schramm (discovered 2002), a main-belt minor planet Schramm–Loewner evolution, a stochastic process in probability...

Nanoparticle tracking analysis Narrow escape problem Osmosis Random walk Schramm–Loewner evolution Single particle trajectories Single particle tracking Statistical...

equations Sea level equation, following post-glacial rebound Schramm–Loewner evolution in statistical mechanics McNary Field, airport in Salem, Oregon...

process Poisson process Compound Non-homogeneous Quasimartingale Schramm–Loewner evolution Semimartingale Sigma-martingale Stable process Superprocess Telegraph...

Löwner-John ellipsoid Schramm–Loewner evolution Loop-erased random walk Systoles of surfaces Berger, Marcel: À l'ombre de Loewner. (French) Ann. Sci. École...

winning the 2007 Abel Prize. In the 1990s and 2000s the theories of Schramm–Loewner evolution and rough paths were introduced and developed to study stochastic...

limit of the self-avoiding walk is conjectured to be described by Schramm–Loewner evolution with parameter κ = ⁠8/3⁠. Critical phenomena – Physics associated...

conformal invariance was proved by Lawler, Oded Schramm and Wendelin Werner (with Schramm–Loewner evolution) in 2004. The cases of four and more dimensions...

triangular lattice, and to its relationship to the Schramm–Loewner evolution introduced by Oded Schramm. He also established conformality for the two-dimensional...

conformal invariance, which relates it in several ways to the Schramm–Loewner evolution, see Sheffield (2005) and Dubédat (2009). Similarly to Brownian...

{\displaystyle \sigma } are represented by stochastic state variables whose time evolution is given by the following system of stochastic differential equations:...

that self-avoiding walks converge in the scaling limit to the Schramm–Loewner evolution. The connective constant is defined as follows. Let c n {\displaystyle...

process Poisson process Compound Non-homogeneous Quasimartingale Schramm–Loewner evolution Semimartingale Sigma-martingale Stable process Superprocess Telegraph...

let z ∈ D be a point. (This is a usual scenario, say, in the Schramm–Loewner evolution). By the Riemann mapping theorem, there is a conformal bijection...

self-similarity and fractional dimension, B. Mandelbrot Lawler, Gregory F.; Schramm, Oded; Werner, Wendelin (2001). "The Dimension of the Planar Brownian Frontier...

"imaginary geometry" which made it possible to integrate the Schramm–Loewner evolution in many GFF fields. Miller and Sheffield also proved that two...

by most later attempts, and is also applied in the theory of Schramm–Loewner evolution. Littlewood (1925, theorem 20) proved that | a n | ≤ e n {\displaystyle...

real number between 8/3 and 8. CLEκ is a loop version of the Schramm–Loewner evolution: SLEκ is designed to model a single discrete random interface...