### Reminder

In all DK related publications, it is required to acknowledge support of the FWF. The following naming convention must be used in all cases:

**Austrian Science Fund (FWF): W1230 **

For example, you may include a sentence such as "The author acknowledges the support of the Austrian Science Fund (FWF): W1230." Please do not forget!

### Project 1:

Random walk models on graphs and groups

#### Publications 2018

[38] | The relation between quenched and annealed Lyapunov exponents in random potential on trees, Stochastic Processes and their Applications, (2018). (to appear)
[bib] [arXiv] [doi/article] | ,

[37] | Boundary representations of Ĺ‚ambda-harmonic and polyharmonic functions on trees, Potential Analysis, (2018). (to appear)
[bib] [arXiv] | ,

[36] | Multidimensional random walk with reflections, Stochastic Processes and their Applications, (2018). (to appear)
[bib] [arXiv] [doi/article] | ,

[35] | Reflected and stopped random walks and the distinguishing number of graphs, PhD thesis, TU Graz, (2018).
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[34] | Distinguishing locally finite trees, (2018). (in preparation)
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[33] | On recurrence of the multidimensional Lindley process, Electronic Communications in Probability, 23(4), 1-14, (2018).
[bib] [arXiv] [doi/article] | ,

#### Publications 2017

[32] | Distinguishing graphs of maximum valence 3, (2017). (submitted)
[bib] [arXiv] | ,

[31] | Random walks on Baumslag-Solitar groups, Israel J. Math, (2017). (to appear)
[bib] [arXiv] | ,

[30] | Oil and water: a two-type internal aggregation model, Annals of Probability, 45(6A), 4019-4070, (2017).
[bib] [arXiv] | ,

#### Publications 2016

[29] | Connectedness and isomorphism properties of the zig-zag product of graphs, J. Graph Theory, 83(2), 120—151, (2016).
[bib] [arXiv] [MR] [doi/article] | ,

[28] | The Cartesian product of graphs with loops, Ars Math. Contemp., 11(1), 1-9, (2016).
[bib] [arXiv] [MR] [doi/article] | ,

[27] | Brownian motion on treebolic space: positive harmonic functions, Ann. Inst. Fourier (Grenoble), 66(4), 1691—1731, (2016).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2015

[26] | Regular sequences and random walks in affine buildings, Ann. Institut Fourier (Grenoble), 65(2), 675-707, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[25] | Combinatorial and probabilistic aspects of discrete groups, PhD thesis, TU Graz, (2015).
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[24] | The Tits alternative for non-spherical triangles of groups, Trans. Lond. Math. Soc., 2(1), 93-124, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[23] | The number of ends of critical branching random walks, ALEA Lat. Am. J. Probab. Math. Stat., 12(1), 55-67, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[22] | Moments of Riesz measures on Poincaré disk and homogeneous tree - a comparative study, Expo. Math., 33(3), 353-374, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[21] | Brownian motion on treebolic space: escape to infinity, Rev. Mat. Iberoam., 31(3), 935-976, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[20] | Relations between cumulants in noncommutative probability, Adv. Math., 282, 56-92, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2014

[19] | Shearer's measure and stochastic domination of product measures, J. Theoret. Probab., 27(1), 22-40, (2014).
[bib] [arXiv] [MR] [doi/article] | ,

[18] | Sufficient conditions for uniform bounds in abstract polymer systems and explorative partition schemes, J. Stat. Phys., 157(6), 1225-1254, (2014).
[bib] [arXiv] [MR] [doi/article] | ,

[17] | Distinguishing graphs with infinite motion and nonlinear growth, Ars Math. Contemp., 7(1), 201-213, (2014).
[bib] [arXiv] [MR] [doi/article] | ,

[16] | Potential theory on infinite trees and the unit disk, PhD thesis, TU Graz, (2014).
[bib] [doi/article] | ,

[15] | Isotropic Markov semigroups on ultra-metric spaces, Uspekhi Mat. Nauk, 69(4(418)), 3-102, (2014). (English original in Russian Math. Surveys 69(4), 589-680, (2014).)
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2013

[14] | Free lamplighter groups and a question of Atiyah, Amer. J. Math., 135(3), 835-849, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[13] | Clique trees of infinite locally finite chordal graphs, (2013). (submitted)
[bib] [arXiv] | ,

[12] | Mean value property for nonharmonic functions, (2013). (preprint)
[bib] [arXiv] | ,

#### Publications 2012

[11] | Properties and applications of Bernoulli random fields with strong dependency graphs, PhD thesis, TU Graz, (2012).
[bib] [doi/article] | ,

[10] | K-independent percolation on trees, Stochastic Process. Appl., 122(3), 1129-1153, (2012).
[bib] [arXiv] [MR] [doi/article] | ,

[9] | The rotor-router group of directed covers of graphs, Electron. J. Combin., 19(3), paper 30, 19 pp., (2012).
[bib] [arXiv] [MR] [doi/article] | ,

[8] | Transience and recurrence of rotor-router walks on directed covers of graphs, Electron. Commun. Probab., 17, paper 41, 13 pp., (2012).
[bib] [arXiv] [MR] [doi/article] | ,

[7] | Internal aggregation models on comb lattices, Electron. J. Probab., 17(30), 1-21, (2012).
[bib] [arXiv] [MR] [doi/article] | ,

[6] | Limit behaviors for random walks and branching random walks on some products of groups, PhD thesis, TU Graz, (2012).
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[5] | Limit behaviors for random walks and branching random walks on some products of groups, PhD thesis, TU Graz, (2012).
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[4] | Branching random walks on free products of groups, Proc. Lond. Math. Soc., 104(6), 1085-1120, (2012).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2011

[3] | Rotor-router aggregation on the comb, Electron. J. Combin., 18(1), paper 224, 23 pp., (2011).
[bib] [arXiv] [MR] [doi/article] | ,

[2] | A noncrossing basis for noncommutative invariants of SL$(2,{\mathbb C})$, J. Combin. Theory Ser. A, 118(1), 257-269, (2011).
[bib] [arXiv] [MR] [doi/article] | ,

[1] | The normal distribution is $\boxplus$-infinitely divisible, Adv. Math., 226(4), 3677-3698, (2011).
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