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M-Ideals in Banach Spaces and Banach Algebras

- P. Harmand, Dirk Werner, W. Werner
- Mathematics
- 26 August 1993

Basic theory of M-ideals.- Geometric properties of M-ideals.- Banach spaces which are M-ideals in their biduals.- Banach spaces which are L-summands in their biduals.- M-ideals in Banach algebras.-… Expand

Conformal invariance of planar loop-erased random walks and uniform spanning trees

- G. Lawler, O. Schramm, W. Werner
- Mathematics
- 20 December 2001

This paper proves that the scaling limit of a loop-erased random walk in a simply connected domain \(D\mathop \subset \limits_ \ne \mathbb{C} \) is equal to the radial SLE2 path. In particular, the… Expand

Conformal restriction: The chordal case

- G. Lawler, O. Schramm, W. Werner
- Mathematics
- 25 September 2002

We characterize and describe all random subsets K of a given simply connected planar domain (the upper half-plane Η, say) which satisfy the conformal restriction” property, i.e., K connects two fixed… Expand

The Brownian loop soup

Abstract.We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary… Expand

Values of Brownian intersection exponents, I: Half-plane exponents

- G. Lawler, O. Schramm, W. Werner
- Physics
- 12 November 1999

Theoretical physics predicts that conformal invariance plays a crucial role in the macroscopic behavior of a wide class of two-dimensional models in statistical physics (see, e.g., [4], [6]). For… Expand

The true self-repelling motion

Abstract. We construct and study a continuous real-valued random process, which is of a new type: It is self-interacting (self-repelling) but only in a local sense: it only feels the self-repellance… Expand

Conformal loop ensembles: the Markovian characterization and the loop-soup construction

- S. Sheffield, W. Werner
- Mathematics
- 11 June 2010

For random collections of self-avoiding loops in two-dimensional domains, we dene a simple and natural conformal restriction property that is conjecturally satised by the scaling limits of interfaces… Expand

CRITICAL EXPONENTS FOR TWO-DIMENSIONAL PERCOLATION

- S. Smirnov, W. Werner
- Mathematics
- 18 September 2001

We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof… Expand

The conformally invariant measure on self-avoiding loops

- W. Werner
- Mathematics
- 24 November 2005

The aim of the present paper is to construct and describe a natural measure on the set of self-avoiding loops in the plane and on any Riemann surface. By a self-avoiding loop on a surface S, we mean… Expand

On the scaling limit of planar self-avoiding walk

- G. Lawler, O. Schramm, W. Werner
- Mathematics
- 23 April 2002

A planar self-avoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no self-intersection. A planar self-avoiding polygon (SAP) is a loop with no self-intersection. In… Expand

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