Browsing by Author "Werner, Wendelin"

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    Drawing large pictures at random : Oberwolfach lecture 2007
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2007) Werner, Wendelin
    This lecture is of very introductory nature. The goal will be to describe specific concrete questions, and to use them as a tool to convey some general ideas. Let me therefore skip the general introduction and immediately start with a first simple question: Is there a way to choose at random and uniformly among all possible choices a continuous curve (a d-dimensional curve, say)?
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    Stochastic Analysis
    (Zürich : EMS Publ. House, 2008) Werner, Wendelin; Zeitouni, Ofer
    [no abstract available]
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    Stochastic Analysis
    (Zürich : EMS Publ. House, 2011) Werner, Wendelin; Zeitouni, Ofer
    The meeting took place on May 30-June 3, 2011, with over 55 people in attendance. Each day had 6 to 7 talks of varying length (some talks were 30 minutes long), except for Thursday: the traditional hike was moved to Thursday due to the weather (and weather on thursday was indeed fine). The talks reviewed directions in which progress in the general field of stochastic analysis occurred since the last meeting of this theme in Oberwolfach three years ago. Several themes were covered in some depth, in addition to a broad overview of recent developments. Among these themes a prominent role was played by random matrices, random surfaces/planar maps and their scaling limits, the KPZ universality class, and the interplay between SLE (Schramm-Loewner equation) and the GFF (Gaussian free field).
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    Stochastic Analysis and Non-Classical Random Processes
    (Zürich : EMS Publ. House, 2005) Werner, Wendelin; Zeitouni, Ofer
    The workshop focused on recent developments in the theory of stochastic processes and flows, with special emphasis on emerging new classes of processes, as well as new objects whose limits are expected to coincide with such processes. A prominent role was played by the SLE family of processes, motion in random media, non-classical noises and flows, and random planar maps.
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    Stochastic Analysis: Around the KPZ Universality Class
    (Zürich : EMS Publ. House, 2014) Hairer, Martin; Werner, Wendelin
    The Gaussian distribution is the “universal” distribution arising in a huge variety of contexts that describes the compound effect of the random fluctuations of many independent (or weakly dependent) sources of randomness that are combined in a (close to) additive way. While this has been very well understood for a long time, the last few years have seen an explosion of results around the “KPZ universality class”, which contains many systems where strongly interacting individual components are combined in a highly non-linear way. In this class, which is still rather poorly understood from a mathematical perspective, fluctuations typically exhibit scaling exponent 1/3 instead of the exponent 1/2 familiar from the central limit theorem and limiting distributions are of Tracy-Widom type rather than Gaussian. This workshop brought together outstanding researchers from a variety of mathematical backgrounds whose areas of research are linked to the understanding of the KPZ equation and universality class. While there are strong links between their motivations, the techniques used by these researchers span a large swath of mathematics, ranging from purely algebraic techniques to renormalisation theory, stochastic analysis, random matrix theory, classical probability theory, orthogonal polynomials, the theory of rough paths, etc.