Point Evaluation of Multi-Variable Random Fractals

Abstract We explore the conjectured duality between a class of large N matrix integrals, known as multicritical matrix integrals (MMI), and the series (2m − 1, 2) of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an S2 topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an S2 and a T2 topology using BRST cohomology considerations. Matrix integrals support this finiteness.

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Probability Density of Random Walks on Random Fractals: Stretched Gaussians and Multifractal Features

Relaxation in Complex Systems and Related Topics - NATO ASI Series ◽

10.1007/978-1-4899-2136-9_41 ◽

1990 ◽

pp. 305-307

Author(s):

H. Eduardo Roman ◽

Armin Bunde ◽

Shlomo Havlin

Keyword(s):

Random Walks ◽

Probability Density ◽

Random Fractals

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The contribution of key observation point evaluation to a scientifically rigorous approach to visual impact assessment

Landscape and Urban Planning ◽

10.1016/j.landurbplan.2018.11.001 ◽

2019 ◽

Vol 183 ◽

pp. 100-110 ◽

Cited By ~ 6

Author(s):

James F. Palmer

Keyword(s):

Impact Assessment ◽

Observation Point ◽

Point Evaluation ◽

Rigorous Approach ◽

Visual Impact ◽

Visual Impact Assessment

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Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

Canadian Mathematical Bulletin ◽

10.4153/cmb-1999-016-x ◽

1999 ◽

Vol 42 (2) ◽

pp. 139-148 ◽

Cited By ~ 59

Author(s):

José Bonet ◽

Paweł Dománski ◽

Mikael Lindström

Keyword(s):

Banach Space ◽

Banach Spaces ◽

Analytic Functions ◽

Composition Operators ◽

Essential Norm ◽

Weak Compactness ◽

Weakly Compact ◽

Point Evaluation ◽

Weighted Banach Spaces ◽

Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

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