CONTENTS -- Preface -- Shigoto nakama de ari yujin de atta kare no omoide -- In Memory of a Colleague and Friend H. Heyer -- In Memory of Professor Shozo Koshi Y. Takahashi -- Recent Developments on Harmonic Forms and L2-Betti Numbers of Infinite Configuration Spaces with Poisson Measures S. Albeverio and A. Daletskii -- 1 Introduction -- 2 De Rham complex over a configuration space -- 3 Von Neumann dimensions of symmetric ten- sor powers of Hilbert spaces -- 4 L2-Betti numbers of configuration spaces of coverings -- References -- Une Reciprocite de Frobenius H. Fujiwara -- 1. INTRODUCTION ET NOTATIONS -- 2. UN LEMME CLEF -- 3. UNE RECIPROCITE DE FROBENIUS -- 4. EXEMPLES -- 5. REMERCIEMENTS -- REFERENCES -- Markov Property of Monotone Levy Processes U. Franz and N. Muraki -- 1. Introduction -- 2. Monotone Independence -- 3. Conditional Expectations -- 4. Monotone LQvy Processes -- 5. The Markov Semigroup of a Monotone LQvy Process -- 6. Examples -- 6.1. Pure drift process -- 6.2. Monotone Brownian motion -- 6.3. Monotone Poisson process -- 7. Martingales -- References -- Geometric Properties of the Set of Extensions of a Stochastic Matrix R. Gohm -- Introduction -- 1. Metric operator spaces and their duals -- 2. Realizations of stochastic matrices -- 3. Extension of states included -- References -- Heat Kernel Analysis on Infinite Dimensional Groups M. Gordina -- 1. MOTIVATION AND HISTORY -- 1.1. Finite-dimensional noncommutative case. -- 1.2. Finite-dimensional commutative case. -- 1.3. Infinite-dimensional commutative case. -- 1.4. New features in the infinite-dimensional noncommutative case. -- 2. NON-COMMUTATIVE LP-SPACES -- 3. STOCHASTIC DIFFERENTIAL EQUATIONS ON L2(M) -- 4. HEAT KERNEL MEASURES -- 5. CAMERON-MARTIN GROUP AND ISOMETRIES. -- REFERENCES -- On Mehler Semigroups, Stable Hemigroups and Selfdecomposability W. Hazod.

1 M-semigroups, stable hemigroups and self-decomposability -- 2 Remarks on root-compactness and embeddability -- 3 Space-time- and background driving processes -- References -- On Infinite Divisibility and Embedding of Probability Measures on a Locally Compact Abelian Group H. Heyer and G. Pap -- 1 Introduction -- 2 Preliminaries -- 3 Gaussian measures -- 4 Continuously embeddable elements -- 5 Examples -- 5.1 Gaussian measures on Rd -- 5.2 Gaussian measures on Td -- 5.3 Gaussian measures on T -- 5.4 Gaussian measures on solenoidal groups -- 6 Weakly infinitely divisible measures -- 7 Embedding property -- 8 Gaussian and diffusion hemigroups -- References -- Character Formula for Wreath Products of Finite Groups with the Infinite Symmetric Group T. Hirai and E. Hirai -- 1. Structure of wreath product groups G (T) -- 1.1. Definition of wreath product G (T) -- 1.2. Standad decomposition and conjugacy classes -- 2. Characters of wreath product group G (T) -- 3. Wreath product of a finite group T with U -- 4. Limits of characters of G (T) as n -- 5. Method of proving Theorem 2.1 -- 6. Inducing up and centralization -- 7. Subgroups and their representations for G (T) -- 8. Increasing sequences of subgroups GN G -- 9. Partial centralization with respect to DJN(T) -- 10. Limits of centralizations -- 11. Criterion for extremality -- 12. Final step of the proof of Theorem 2.1 -- Acknowledgements -- References -- Remark on Biane's Character Formula and Concentration Phenomenon in Asymptotic Representation Theory A . Hora -- 1. Introduction -- 2. A Preparatory Trace Formula -- 2.1. Transition measure of a diagram -- 2.2. A trace formula -- 3. Biane's Formula for Irreducible Characters -- 3.1. Biane 's asymptotic formula -- 3.2. Proof of Biane's formula -- 3.3. Auxiliary estimates -- 4. Concentration Phenomenon -- 4.1. Scheme of concentration phenomenon.

4.2. Asymptotic factorization for Jucys-Murphy operators -- References -- Real Hardy Spaces on Real Rank 1 Semisimple Lie Groups T. Kawazoe -- 1. Introduction -- 2. Notation -- 3. Radial maximal functions -- 4. Real Hardy spaces -- 5. Atomic Hardy spaces -- 6. Characterization of H1 (G//K) -- References -- White Noise Analysis, Filtering Equation and the Index Theorem for Families R. Le'andre -- I. Introduction -- II. Partial Malliavin Calculus -- III. Bismut-Witten current -- References -- Laplace Approximations for Diffusion Processes S. Liang -- 1 The problems -- 2 The case for diffusions on tori -- 3 The case for diffusions on Euclidean spaces -- 4 Examples -- References -- A Note on Afine Quotients and Equivariant Double Fibrations K. Nishiyama -- Introduction -- 1. Preliminaries -- 1.1. Special linear group -- 1.2. General linear group -- 1.3. Quadratic space -- 2. Equivariant double fibration -- 3. Double fibration related to the natural representations -- 3.1. Tensor products -- 3.2. Contraction by the action of a general linear group -- 4. Application to Dokovit-Sekiguchi-Zhao problem -- 4.1. Resolution via the contmction by the action of GL(n, C) -- 4.2. Resolution via the action of the orthogonal and symplectic groups -- References -- Admissible White Noise Operators and Their Quantum White Noise Derivatives U. C. Ji and N. Obata -- 1. Introduction -- 2. White Noise Theory -- 2.1. Underlying Gelfand rriple -- 2.2. Hida-Kubo-Takenaka Space -- 2.3. White Noise Operators -- 2.4. Gaussian Realization -- 3. Admissible White Noise Operators -- 3.1. Admissible White Noise Functions -- 3.2. Admissible White Noise Operators -- 3.3. Admissible White Noise Opemtors with Supporter -- 4. Quantum White Noise Derivatives -- 4.1. lhnslation Opemtor -- 4.2. Gross Derivative -- 4.3. Annihilation- and Creation- Derivatives.

4.4. Fock Expansion of an Admissible Opemtor -- 4.5. QWN-Derivatives of an Admissible Operator -- 4.6. Pointwise QWN-Derivatives -- References -- PDE Approach to Invariant and Gibbs Measures with Applications M. Rockner -- 1. Introduction -- 2. The PDE-approach to invariant and Gibbs measures -- 2.1. The finite dimensional case -- 2.2. The infinite dimensional case -- 3. Infinitesimally invariance implies Gibbsian -- 4. Application -- Acknowledgement -- References -- Deformations of Convolution Semigroups on Commutative Hypergroups M. Rosler and M. Voit -- 1. Introduction -- 2. Deformations of commutative hypergroups -- 3. Deformation of convolution semigroups -- References -- An Infinite Dimensional Laplacian Acting on Multiple Wiener Integrals by Some Levy Processes K. Suito -- Introduction -- 1 Functionals of Gaussian noise and Poisson noise -- 2 The Levy Laplacian acting on multiple Wiener integrals -- 3 The Levy Laplacian acting on WNF-valued functions -- 4 An infinite dimensional stochastic process associated with the Levy Laplacian -- Acknowledgments -- References -- Levy Processes on Deformations of Hopf Algebras M. Schurmann -- References -- Unitary Representations of the Group of Diffeomorphisms via Restricted Product Measures with Infinite Mass H. Shimomura (joint work with T. Hirai) -- 1. Introduction -- 2. Basic Discussions -- 2.1. Restricted product measure with infinite mass -- 2.2 Action of Diff0(M) from the left and of G from the right -- 2.3 Representation space H( ) -- 3. Irreducibility -- 4. Equivalence -- References -- An Application of the Method of Moments in Random Matrix Theory M. Stolz -- 1. Moments and Weak Convergence -- 2. Application to Random Matrices -- References -- Isotropy Representation for Harish-Chandra Modules H. Yamashita -- 1. Introduction -- 2. Graded module grX and induced representation r(W).

2.1. Associated cycle and isotropy repwsentation -- 2.2. Induced module r(Z) -- 2.3. Homomorphism T = T(j) -- 2.4. IIrreducibility -- 2.5. Case of unitary highest weight representations -- 3. Utility of the dual (S(g), Kc)-module -- 3.1. Kc-finite dual M* and its submodule -- 3.2. A suflcient condition for I = Anns(g)M -- 3.3. Difleerential opemtor of gmdient type -- 4. Isotropy representation attached to discrete series -- 4.1. Discrete series -- 4.2. Results of Hotta-Parthasamthy -- 4.3. Description of associated cycle -- 4.4. Submodule U (Qc) -- 4.5. Relation to the Richardson orbit -- 4.6. Condition (Cl) for SU(p, q ) -- Acknowledgments -- References.