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Brownian excursion measure — 1 results found.

      
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The scaling limit of Fomin’s identity for two paths in the plane
C. R. Math. Rep. Acad. Sci. Canada Vol. 29 (3) 2007, pp. 65–80
Michael J. Kozdron (Received: 2007/08/11)

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We review some recently completed research that establishes the scaling limit of Fomin’s identity for loop-erased random walk on \(\mathbb{Z}^2\) in terms of the chordal Schramm–Loewner evolution (SLE) with parameter \(2\). In the case of two paths, we provide a simplified proof of the identity for loop-erased random walk and simple random walk, and prove directly that the corresponding identity holds for chordal \(\operatorname{SLE}_2\) and Brownian motion. We also include a brief introduction to SLE and discussion of the relationship between \(\operatorname{SLE}_2\) and loop-erased random walk.

Nous passons en revue de la recherche récemment réalisée qui établit la limite de l’identité de Fomin pour la marche aléatoire à boucles effacées sur \(\mathbb{Z}^2\) en termes du processus Schramm–Loewner (où SLE pour Schramm–Loewner evolution) avec paramètre 2. Dans le cas de deux chemins, nous fournissons une preuve simplifiée de l’identité pour la marche aléatoire à boucles effacées et la marche aléatoire simple, et prouvons ordonner que l’identité correspondante se tient pour \(\operatorname{SLE}_2\) et le mouvement brownien. Nous incluons également une brève introduction au processus Schramm–Loewner et une discussion du rapport entre \(\operatorname{SLE}_2\) et la marche aléatoire à boucles effacées.

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

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