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Search Results: 1 - 10 of 2454 matches for " Franz Lehner "
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On party competition and government overload
Franz Lehner
Philosophica , 1977,
On the Eigenspaces of Lamplighter Random Walks and Percolation Clusters on Graphs
Franz Lehner
Mathematics , 2008, DOI: 10.1090/S0002-9939-09-09869-4
Abstract: We show that the Plancherel measure of the lamplighter random walk on a graph coincides with the expected spectral measure of the absorbing random walk on the Bernoulli percolation clusters. In the subcritical regime the spectrum is pure point and we construct a complete orthonormal basis of finitely supported eigenfunctions.
On the computation of spectra in free probability
Franz Lehner
Mathematics , 2000, DOI: 10.1006/jfan.2001.3748
Abstract: We use free probability techniques to compute borders of spectra of non hermitian operators in finite von Neumann algebras which arise as `free sums' of `simple' operators. To this end, the resolvent is analyzed with the aid of the Haagerup inequality. Concrete examples coming from reduced C*-algebras of free product groups and leading to systems of polynomial equations illustrate the approach.
Cumulants in noncommutative probability II. Generalized Gaussian random variables
Franz Lehner
Mathematics , 2002, DOI: 10.1007/s00440-003-0292-0
Abstract: We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.
Free cumulants and enumeration of connected partitions
Franz Lehner
Mathematics , 2001, DOI: 10.1006/eujc.2002.0619
Abstract: A combinatorial formula is derived which expresses free cumulants in terms of classical comulants. As a corollary, we give a combinatorial interpretation of free cumulants of classical distributions, notably Gaussian and Poisson distributions. The latter count connected pairings and connected set partitions respectively. The proof relies on Moebius inversion on the partition lattice.
Cumulants, lattice paths, and orthogonal polynomials
Franz Lehner
Mathematics , 2001, DOI: 10.1016/S0012-365X(02)00834-8
Abstract: A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions and Lagrange inversion. For the converse we discuss Gessel-Viennot theory to express Hankel determinants in terms of various cumulants.
Cumulants in noncommutative probability I. Noncommutative Exchangeability Systems
Franz Lehner
Mathematics , 2002, DOI: 10.1007/s00209-004-0653-0
Abstract: Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting.It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the formula says that cumulants are moments of a certain ``discrete Fourier transform'' of a random variable. This provides a simple unified method to understand the known examples of cumulants, like classical, free cumulants and various q-cumulants.
Cumulants in Noncommutative Probability Theory III. Creation- and annihilation operators on Fock spaces
Franz Lehner
Mathematics , 2002, DOI: 10.1142/S0219025705002049
Abstract: Fock space constructions give rise to natural exchangeable families and are thus well suited for cumulant calculations. In this paper we develop some general formulas and compute cumulants for generalized Toeplitz operators, notably for q-Fock spaces, previously considered by M. Anshelevich and A. Nica, and Fock spaces for characters of the infinite symmetric group, which where constructed by Bozejko and Guta. An expression for cumulants in terms of the cycle-cover polynomials of certain directed graphs is obtained in this case.
A Noncrossing Basis for Noncommutative Invariants of SL(2,C)
Franz Lehner
Mathematics , 2009, DOI: 10.1016/j.jcta.2010.06.004
Abstract: Noncommutative invariant theory is a generalization of the classical invariant theory of the action of $SL(2,\IC)$ on binary forms. The dimensions of the spaces of invariant noncommutative polynomials coincide with the numbers of certain noncrossing partitions. We give an elementary combinatorial explanation of this fact by constructing a noncrossing basis of the homogeneous components. Using the theory free stochastic measures this provides a combinatorial proof of the Molien-Weyl formula in this setting.
Cumulants as iterated integrals
Franz Lehner
Mathematics , 2009, DOI: 10.1016/j.jspi.2010.10.011
Abstract: A formula expressing cumulants in terms of iterated integrals of the distribution function is derived. It generalizes results of Jones and Balakrishnan who computed expressions for cumulants up to order 4.
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