Prof. Dr. Adam Timar

Former Bonn Junior Fellow
Subsequent positions: Assistant Professor, University of Szeged
Marie Curie fellow at Renyi Institute, Budapest

E-mail: madaramit(at)
Institute: Institute for Applied Mathematics

Academic Career

2002 - 2006

PhD, Indiana University, Bloomington, IN, USA

2006 - 2008

Postdoctoral Fellow, University of British Columbia, Vancouver, BC, Canada

2008 - 2011

Professor (W2, Bonn Junior Fellow), University of Bonn

Assistant Professor, University of Szeged, Hungary

Research Profile

One of my interests has been the interplay of probabilistic models and geometric group theory. I have been working on the questions of how critical probabilities (for the existence of one, or of infinitely many infinite clusters) and critical exponents behave for Cayley graphs of various properties (in particular, what is preserved by quasi-isometries). In [7], we introduce a new coarse-geometric invariant, the separation profile of groups, giving rise to several questions (e.g., what separation functions may arise for a Cayley graph?) that I would like to investigate further. Another focus of my interests is stochastic optimization problems in an infinite setup. We have recently found an allocation rule of optimal tail for the Poisson point process, but work is still in progress on whether it can be applied to give optimal matching rules, and whether the allocation rule can be generated in some “canonical” way (as in case of gravitational allocation).

Contribution to Research Areas

Research Area G
I have worked on random invariant subgraphs of infinite transitive graphs (percolation, random forests), the most important example for the underlying graph being Cayley graphs. In [1], [2], [3], [4], we investigate some properties of Bernoulli percolation and wired minimal spanning forests on nonamenable graphs; in [5], I generalize and simplify some tools that are frequently used for Peierls type arguments, hence making them available for percolation beyond usual euclidean lattices.
The question of factors is important in the study of random subgraphs of transitive graphs, but also in case of invariant point processes in some space. Matching, allocation and coloring questions here are among my interests (see [6] and submitted preprints).

Selected Publications

[1] �dám Timár
Percolation on nonunimodular transitive graphs
Ann. Probab. , 34: (6): 2344--2364
DOI: 10.1214/009117906000000494
[2] Adám Timár
Neighboring clusters in Bernoulli percolation
Ann. Probab. , 34: (6): 2332--2343
DOI: 10.1214/009117906000000485
[3] �dám Timár
Ends in free minimal spanning forests
Ann. Probab. , 34: (3): 865--869
DOI: 10.1214/009117906000000025
[4] Antar Bandyopadhyay, Jeffrey Steif, �dám Timár
On the cluster size distribution for percolation on some general graphs
Rev. Mat. Iberoam. , 26: (2): 529--550
DOI: 10.4171/RMI/608

Publication List

MathSciNet Publication List (external link)

Selected PhD students

Roland Marko

Supervised Theses

  • Diplom theses: 2, currently 2
  • PhD theses: 1, currently 1
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