What we celebrate today as crafts were once the means of everyday manufacture. The craftsman's product was not quaint, archaic, or merely decorative-it was essential. The tools that created these necessities speak to the early American spirit of ingenuity. Simple but resourceful, each tool was a beautiful, clever marriage of form and function, endowed with a life of its own, uniquely forged and perfectly suited for its purpose. The Landis Valley Village & Farm Museum, the leading public attraction devoted to Pennsylvania German ("Pennsylvania Dutch") culture, works to preserve and carry the art of handcrafts into the modern age by educating and delighting visitors with their vast collection and craftwork demonstrators often in authentic dress, using period tools. With this book, the museum celebrates the hand tool as a medium of expression and salutes those who wield it with skillful pride. Through hundreds of images of these elegantly purposeful hand tools, the history of American handcraft is traced-sure to delight the luddite at heart.

Kunita, H.: Stochastic differential equations and stochastic flows of diffeomorphisms.-Elworthy, D.: Geometric aspects of diffusions on manifolds.-Ancona, A.: Theorie du potential sur les graphs et les varieties.-Emery, M.: Continuous martingales in differentiable manifolds.

Nine volumes ago, in S eminaire de Probabilit es XXXIII, a series of advanced courses was started; nine such courses have appeared since. Two of them are due to Antoine Lejay, including his Introduction to rough paths in v- umeXXXVII. Thisunrepentantrecidivistnowstrikesagain, withYetanother introduction to rough paths, which sheds a more algebraic light on the same matter. The various contributions which constitute the rest of the volume ex- plify the r ole the S eminaire intends to play on the probabilistic stage: junior authors go side by side with older contributors, with a predominance from French or francophile ones; short notes mix with real research articles; and the themes are well in the traditional spirit of the S eminaire, ranging over the broad spectrum of interest of the readership of the S eminaire. Catherine Donati-Martin, Michel Emery, Alain Rouault, Christophe Stricker vii Contents Yet Another Introduction to Rough Paths Antoine Lejay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Monotonicity of the Extremal Functions for One-dimensional Inequalities of Logarithmic Sobolev Type Laurent Miclo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Non-monotone Convergence in the Quadratic Wasserstein Distance Walter Schachermayer, Uwe Schmock, and Josef Teichmann. . . . . . . . . . 131 On the Equation ? =S t t Fangjun Xu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Shabat Polynomials and Harmonic Measure Philippe Biane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Radial Dunkl Processes Associated with Dihedral Systems Nizar Demni. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Matrix Valued Brownian Motion and a Paper by P olya Philippe Biane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 On the Laws of First Hitting Times of Points for One-dimensional Symmetric Stable L evy Processes Kouji Yano, Yuko Yano, and Marc Yor. . . . . . . . . . . . . . . . . . . . . . . . . . . . ."

Stochastic processes are as usual the main subject of the Seminaire, with contributions on Brownian motion (fractional or other), Levy processes, martingales and probabilistic finance. Other probabilistic themes are also present: large random matrices, statistical mechanics. The contributions in this volume provide a sampling of recent results on these topics. All contributions with the exception of two are written in English language.

Who could have predicted that the S eminaire de Probabilit es would reach the age of 40? This long life is ?rst due to the vitality of the French probabil- tic school, for which the S eminaire remains one of the most speci?c media of exchange. Another factor is the amount of enthusiasm, energy and time invested year after year by the R edacteurs: Michel Ledoux dedicated himself tothistaskuptoVolumeXXXVIII,andMarcYormadehisnameinseparable from the S eminaire by devoting himself to it during a quarter of a century. Browsing among the past volumes can only give a faint glimpse of how much is owed to them; keeping up with the standard they have set is a challenge to the new R edaction. In a changing world where the status of paper and ink is questioned and where, alas, pressure for publishing is increasing, in particular among young mathematicians, we shall try and keep the same direction. Although most contributions are anonymously refereed, the S eminaire is not a mathema- cal journal; our ?rst criterion is not mathematical depth, but usefulness to the French and international probabilistic community. We do not insist that everything published in these volumes should have reached its ?nal form or be original, and acceptance-rejection may not be decided on purely scienti?c grounds.

The 39th volume of S minaire de Probabilit?'s is a tribute to the memory of Paul Andr Meyer. His life and achievements are recalled in this book, and tributes are paid by his friends and colleagues. This volume also contains mathematical contributions to classical and quantum stochastic calculus, the theory of processes, martingales and their applications to mathematical finance and Brownian motion. These contributions provide an overview on the current trends of stochastic calculus.

Besides a series of six articles on Levy processes, Volume 38 of the Seminaire de Probabilites contains contributions whose topics range from analysis of semi-groups to free probability, via martingale theory, Wiener space and Brownian motion, Gaussian processes and matrices, diffusions and their applications to PDEs.

As do all previous volumes of this series, it provides an overview on the current state of the art in the research on stochastic processes.

The 37th SA(c)minaire de ProbabilitA(c)s contains A. Lejay's advanced course which is a pedagogical introduction to works by T. Lyons and others on stochastic integrals and SDEs driven by deterministic rough paths. The rest of the volume consists of various articles on topics familiar to regular readers of the SA(c)minaires, including Brownian motion, random environment or scenery, PDEs and SDEs, random matrices and financial random processes.

The 36th Séminaire de Probabilités contains an advanced course on Logarithmic Sobolev Inequalities by A. Guionnet and B. Zegarlinski, as well as two shorter surveys by L. Pastur and N. O'Connell on the theory of random matrices and their links with stochastic processes. The main themes of the other contributions are Logarithmic Sobolev Inequalities, Stochastic Calculus, Martingale Theory and Filtrations. Besides the traditional readership of the Séminaires, this volume will be useful to researchers in statistical mechanics and mathematical finance.

The 31 papers collected here present original research results obtained in 1995-96, on Brownian motion and, more generally, diffusion processes, martingales, Wiener spaces, polymer measures.

The volume consists entirely of research papers, principally in stochastic calculus, martingales, and Brownian motion, and gathers an important part of the works done in the main probability groups in France (Paris, Strasbourg, Toulouse, Besan on, Grenoble, ...) together with closely related works done by some probabilists elsewhere (Switzerland, India, Austria, ...)

All the papers included in this volume are original research papers. They represent an important part of the work of French probabilists and colleagues with whom they are in close contact throughout the world. The main topics of the papers are martingale and Markov processes studies.

Addressed to both pure and applied probabilitists, including graduate students, this text is a pedagogically-oriented introduction to the Schwartz-Meyer second-order geometry and its use in stochastic calculus. P.A. Meyer has contributed an appendix: "A short presentation of stochastic calculus" presenting the basis of stochastic calculus and thus making the book better accessible to non-probabilitists also. No prior knowledge of differential geometry is assumed of the reader: this is covered within the text to the extent. The general theory is presented only towards the end of the book, after the reader has been exposed to two particular instances - martingales and Brownian motions - in manifolds. The book also includes new material on non-confluence of martingales, s.d.e. from one manifold to another, approximation results for martingales, solutions to Stratonovich differential equations. Thus this book will prove very useful to specialists and non-specialists alike, as a self-contained introductory text or as a compact reference.

Twenty-five articles have been selected from the first 14 volumes of the "SA(c)minaire de ProbabilitA(c)s," all out of print, for their historical and/or mathematical interest. Among the many articles devoted to Martingale theory in the early volumes of the SA(c)minaire, we have chosen to reprint those that are particularly significant from a historical point of view, as well as those that can still be useful today. They are reprinted here verbatim, with a short retrospective comment, for the benefit of researchers in the theory of stochastic processes, in mathematical finance, or in history of mathematics.

All the papers in the volume are original research papers, discussing fundamental properties of stochastic processes. The topics under study (martingales, filtrations, path properties, etc.) represent an important part of the current research performed in 1996-97 by various groups of probabilists in France and abroad.

Description: Hiru was an ordinary half-Asian, half-European male, with a long list of interests, a loving mother, and a father that provided substantial income. Yet, his life changes for the worst when his first experiences with werewolves begin. His experiences continue, as he travels to Japan in search of answers, killing werewolves and experiencing various other practices, on the way. Warning: Depicts scenes of violence, sexual themes and horror. Therefore, should not be read by person under the age of 18. No seriously, it can be very disturbing. Audience: 18+ Preview: First Chapter Series: Possibly part of a two book series. Book no.: 1