Vladas Sidoravicius - Böcker

The intersection of probability and physics has been a rich and explosive area of growth in the past two decades. This volume contains invited articles by leading probabilists highlighting these advances. Major areas covered include: percolation theory, random walks, interacting particle systems and topics related to statistical mechanics. Graduate students and researchers in probability theory and math physics should find this book a useful reference. In the last several years, substantial progress has been made in a number of directions: fluctuations of 2-dimensional growth processes; Wulf constructions in higher dimensions for percolation; Potts and Ising models; classification of random walks in random environments; the introduction of the stochastic Loewner equation; the rigorous proof of intersection exponents for planar Brownian motion; and finally the proof of conformal invariance for critical percolation on the triangular lattice. This volume consists of a collection of invited articles, written by probabilists in the above-mentioned areas, most of whom were personally responsible for advances in the various subfields of probability.All of the articles are an outgrowth of the Fourth Brazilian School of Probability, held in Mambucaba, Brazil, August 2000. The contributors are K. Alexander, J. van den Berg, T. Bodineau, F. Camia, N. Cancrini, G. Grimmett, P. Hiemer, A.E. Holroyd, H. Kesten, G.F. Lawler, T.M. Liggett, J. Lorinczi, F. Martinelli, C.M. Newman, J. Quastel, C.-E. Pfister, M. Prahofer, C. Roberto, O. Schramm, V. Sidoravicius, H. Spohn, A. Toom, B. Toth, D. Ueltschi, W. Werner, M. Wschebor and M. Wuthrich.

For more than two decades percolation theory, random walks, interacting parti­ cle systems and topics related to statistical mechanics have experienced inten­ sive growth. In the last several years, especially remarkable progress has been made in a number of directions, such as: Wulff constructions above two dimen­ sions for percolation, Potts and Ising models, classification of random walks in random environments, better understanding of fluctuations in two dimen­ sional growth processes, the introduction and remarkable uses of the Stochastic Loewner Equation, the rigorous derivation of exact intersection exponents for planar Brownian motion, and finally, the proof of conformal invariance for crit­ ical percolation scaling limits on the triangular lattice. It was thus a fortuitous time to bring together researchers, including many personally responsible for these advances, in the framework of the IVth Brazilian School of Probability, held at Mambucaba on August 14-19,2000. This School, first envisioned and organized by IMPA's probability group in 1997, has since developed into an annual meeting with an almost constant format: it usually offers three advanced courses delivered by prominent scientists, combined with a high-level conference. This volume contains invited articles associated with that meeting, and we hope it will provide the reader with an accurate impression regarding the current state of affairs in these important fields of probability theory.

This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical understanding of phenomena describing systems in highly inhomogeneous and disordered media, including the KPZ universality class (describing the evolution of interfaces in two dimensions), random walks in random environment and percolative systems. PASI fosters a collaboration between North American and Latin American researchers and students. The conference that inspired this volume took place in January 2012 in both Santiago de Chile and Buenos Aires. Researchers and graduate students will find timely research in probability theory, statistical physics and related disciplines.

This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical understanding of phenomena describing systems in highly inhomogeneous and disordered media, including the KPZ universality class (describing the evolution of interfaces in two dimensions), random walks in random environment and percolative systems. PASI fosters a collaboration between North American and Latin American researchers and students. The conference that inspired this volume took place in January 2012 in both Santiago de Chile and Buenos Aires. Researchers and graduate students will find timely research in probability theory, statistical physics and related disciplines.

This volume celebrates the tenth edition of the Brazilian School of Probability (EBP), held at IMPA, Rio de Janeiro, from July 30 to August 4, 2006, jointly with the 69th Annual Meeting of the Institute of Mathematical Statistics. It was indeed an exceptional occasion for the local community working in this ?eld. The EBP, ?rst envisioned and organized in 1997, has since developed into an annual meeting with two or three advanced mini-courses and a high level conference. This volume grew up from invited or contributed articles by researchers that during the last ten yearshave been participating in the BrazilianSchool of Pro- bility. As a consequence, its content partially re?ects the topics that have pred- inated in the activities during the various editions of the School, with a strong - peal that comes from statistical mechanics and areasof concentrationthat include interacting particlesystems, percolation, random media anddisordered systems. All articles of this volume were peer-refereed.

The XV-th International Congress on Mathematical Physics took place in Rio de Janeiro, on August 5-11, 2006. I believe it was a very successful and enjoyable meeting. It is very fortunate for our community that Latin America, and especially Brazil, in decades has become the place where all ?elds of intellectual activity which are traditionally regarded as part of Mathematical Physics are developing with steady pace and remarkable quality. Another important aspect of this devel- mentis thatbesidesareaswhichalreadyhaveworldwiderecognitionandlongsta- ing tradition in Brazil such as Dynamical Systems, Statistical Mechanics, Probab- ity Theory, etc. , there is intensive growth in other directions such as String Theory and Algebraic Geometry. Brazil's major universities and research institutes such as IMPA and CBPF are successfully bringing up a new generation of researchers in our ?eld. Thus it was especially pleasant to see that among more than 500 participants of the Congress, the majority was constituted by young researchers and graduate students. Given the enormous range of subjects covered during the Congress, and the - versity of scienti?c contributions, it would be pointless to summarize the contents here-the quality is re?ected in these pages. Traditionally, besides its very intense scienti?c program, the Congress was the occasion for the award of the Henri Poincare Prizes of the IAMP, sponsored by the Daniel Iagolnitzer Foundation. The Laureates for the year 2006 were Ludwig Faddeev, David Ruelle and Edward Witten.

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century.  This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday.The sub-titles of the three volumes are: I.   Spin Glasses and Statistical MechanicsII.  Brownian Web and PercolationIII. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century.  This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday.The sub-titles of the three volumes are:I.   Spin Glasses and Statistical MechanicsII.  Brownian Web and PercolationIII. Interacting Particle Systems and Random WalksThe articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Interacting Particle Systems and Random WalksThe articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century.  This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday.The sub-titles of the three volumes are:I.   Spin Glasses and Statistical MechanicsII.  Brownian Web and PercolationIII. Interacting Particle Systems and Random WalksThe articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.