Random Fields I

Prof. Dr. Evgeny Spodarev

Teaching Assistant
Daniel Meschenmoser

Time and Place

Thursday 12:30 - 14:00 (without break) in E60 (Helmholtzstrasse 18)

Exercise Session
Thursday 16 - 18 in E60 (Helmholtzstrasse 18)


2 hours lecture + 2 hours exercises


Probability Calculus

Intended Audience

Bachelor / Master students in Mathematics and Business Mathematics


This course provides an introduction to random surfaces (so-called fields) which are random processes with spatial index.

The main topics are:

  • Kolmogorov's existence theorem
  • Stationarity and isotropy
  • Correlation theory
  • Basic models of random fields

The course will be taught in English.

Requirements to obtain the certificate (Übungsschein)

In order to obtain the certificate, one has to earn 50% of all homework credits.

Exercise sheets


  • Adler, R. J., Taylor, J. E.: Random Fields and Geometry, Springer, 2007
  • Azais, J.-M., Wschebor, M.: Level Sets and Extrema of Random Processes and Fields, Wiley, 2009
  • Bogachev, V.I.: Gaussian Measures, AMS, 1998
  • Brémaud, P.: Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues, Springer, 1999
  • Bulinski, A., Shashkin, A.: Limit Theorems for Associated Random Fields and Related Systems, World Scientific, 2007
  • Dudley, R. M.: Uniform Central Limit Theorems, Cambridge Univ. Pr.,1999
  • Fernique, X: Fonctions aléatoires gaussiennes vecteurs aléatoires gaussiens, CRM, Montreal, 1997
  • Georgii, H.-O.: Gibbs Measures and Phase Transitions, de Gruyter, Berlin, 1988
  • Guyon, X.: Random Fields on a Network, Springer, 1995
  • Ivanov, A.V., Leonenko, N.N.: Statistical Analysis of Random Fields, Kluwer, 1989
  • Ledoux, M., Talagrand, M.: Probability in Banach Spaces: Isoperimetry and Processes, Springer, 1991
  • Leonenko, M.: Limit Theorems for Random Fields with Singular Spectrum, Kluwer, 1999
  • Lifshits, M.A.: Gaussian Random Functions, Kluwer, 1995
  • Khoshnevisan, D.: Multiparameter Processes: An Introduction to Random Fields, Springer, 2002
  • Malyshev, V. A., Minlos, R. A.: Gibbs Random Fields: Cluster Expansions, Kluwer, 1991
  • Piterbarg, V. I.: Asymptotic Methods in the Theory of Gaussian Processes and Fields, AMS, 1996
  • Ramm, A.: Random Fields Estimation, World Scientific, 2005
  • Yaglom, A. M.: Correlation Theory of Stationary and Related Random Functions, Volume I,Springer, 1987
  • Yaglom, A. M.: Correlation Theory of Stationary and Related Random Functions, Volume II, Springer, 1987

(download: pdf)



Teaching Assistant