Name | Dr. Wendelin Werner |

URL | http://www.math.ethz.ch/~wewerner |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-3601-00L | Probability Theory At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office (Link) after having received the credits. | 10 credits | 4V + 1U | W. Werner | |

Abstract | Basics of probability theory and the theory of stochastic processes in discrete time | ||||

Objective | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, series of independent random variables, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson processes, Markov chains (classification and convergence results). | ||||

Content | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson processes, Markov chains (classification and convergence results). | ||||

Lecture notes | will be available in electronic form. | ||||

Literature | R. Durrett, Probability: Theory and examples, Duxbury Press 1996 H. Bauer, Probability Theory, de Gruyter 1996 J. Jacod and P. Protter, Probability essentials, Springer 2004 A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006 D. Williams, Probability with martingales, Cambridge University Press 1991 | ||||

401-4600-71L | Student Seminar in ProbabilityLimited number of participants. Registration to the seminar will only be effective once confirmed by email from the organisers. This Student Seminar in Probability will be at an advanced level (dealing with current research topics), and the participants will be at a doctoral level or postdocs. Of course, non-participants are welcome to attend the various talks of the seminar. | 4 credits | 2S | J. Bertoin, V. Tassion, W. Werner | |

Abstract | |||||

Objective | |||||

Content | The seminar is centered around a topic in probability theory which changes each semester. | ||||

Prerequisites / Notice | The student seminar in probability is held at times at the undergraduate level (typically during the spring term) and at times at the graduate level (typically during the autumn term). The themes vary each semester. The number of participants to the seminar is limited. Registration to the seminar will only be effective once confirmed by email from the organizers. | ||||

401-4607-67L | Schramm-Loewner Evolutions | 4 credits | 2V | W. Werner | |

Abstract | This advanced course will be an introduction to SLE (Schramm-Loewner Evolutions), which are a class of conformally invariant random curves in the plane. We will discuss their construction and some of their main properties. | ||||

Objective | |||||

Prerequisites / Notice | Knowledge of Brownian motion and stochastic calculus and basic knowledge of complex analysis (Riemann's mapping theorem). Familiarity of lattice models such as percolation or the Ising model can be useful but not necessary. | ||||

401-5600-00L | Seminar on Stochastic Processes | 0 credits | 1K | J. Bertoin, A. Nikeghbali, B. D. Schlein, V. Tassion, W. Werner | |

Abstract | Research colloquium | ||||

Objective |