## Publications and Preprints

- with M. Disertori and F. Merkl:

The non-linear supersymmetric hyperbolic sigma model on a complete graph with hierarchical interactions Preprint on arxiv^{} - with D. Conache, M. Heydenreich
^{}and F. Merkl:

*Variance of voltages in a lattice Coulomb gas*. Accepted for publication in Journal of Statistical Physics^{}Preprint on arxiv^{} - with F. Merkl and P. Tarrès:

*Random interlacements for vertex-reinforced jump processes*. Annales de l’Institut Henri Poincaré^{}. Vol. 57, No. 2, 1058-1080, 2021. Preprint on arxiv^{} - with R. Bauerschmidt
^{}, D. Conache, M. Heydenreich^{}and F. Merkl:

*Dislocation lines in three-dimensional solids at low temperature*.

Annales Henri Poincaré^{}, 20, 3019–3057, 2019. Article^{}Preprint on arxiv^{} - with F. Merkl and P. Tarrès:

*Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model.*

Probability theory and related fields^{}, Volume 173, Issue 3–4, pp 1349–1387, 2019. Article^{}Preprint on arxiv^{} - with M. Disertori and F. Merkl:

*Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model*

ALEA^{}Lat. Am. J. Probab. Math. Stat., volume XVI, 179-209, 2019. Article^{} - with M. Disertori and F. Merkl:

*A supersymmetric approach to martingales related to the vertex-reinforced jump process.*

ALEA^{}Lat. Am. J. Probab. Math. Stat., 14, 529-555, 2017. Article^{} - with M. Disertori and F. Merkl:

*A comparison of the nonlinear sigma model with general pinning and pinning at one point.*

Electronic Journal of probability^{}, 21, Paper no. 27, 1-16, 2016. Article^{}. - with Markus Heydenreich
^{}and F. Merkl:

*Spontaneous breaking of rotational symmetry in the presence of defects.*

Electronic Journal of probability^{}, 19, Paper no. 111, 1-17, 2014. Article^{}. - with M. Disertori and F. Merkl:

*Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes.*

Communications in Mathematical Physics^{}December 2014, Volume 332, Issue 2, 783-825. Article^{}Preprint on arxiv - with F. Merkl:

*Perturbation analysis of the van den Berg Kesten inequality for determinantal probability measures.*

Electronic Journal of probability^{}, 18, Paper no. 92, 1-20, 2013. Article^{}. - with F. Merkl:

*Correlation inequalities for edge-reinforced random walk.*

Electronic Communications in Probability, 16, Paper no. 66, 753-763, 2011. Article - with F. Merkl:

*Spontaneous breaking of continuous rotational symmetry in two dimensions.*

Electronic Journal of Probability, 14, Paper no. 57, 1705-1726, 2009. Article - with M. Eckhoff:

*Uniqueness of the mixing measure for a random walk in a random environment on the positive integers.*

Electronic communications in probability, 14, 31-35, 2009. Article - with F. Merkl:

*Recurrence of edge-reinforced random walk on a two-dimensional graph.*

The Annals of Probability, 37 (2009) 5, 1679-1714. Article - with F. Merkl:

*Edge-reinforced random walk on one-dimensional periodic graphs.*

Probability Theory and Related Fields, 145 (2009) 3-4, 323-349. Article - with F. Merkl and A. Öry:

*The "magic formula" for linearly edge-reinforced random walks.*

Statistica Neerlandica (2008) Volume 62, nr. 3, 345-363. Article - with F. Merkl:

*Bounding a random environment for two-dimensional edge-reinforced random walk.*

Electronic Journal of Probability, 530-565, 2008. Article - with F. Merkl:

*A random environment for linearly edge-reinforced random walks on infinite graphs.*

Probability Theory and Related Fields, 138 (2007) 1-2, 157-176. Article - with F. Merkl:

*Asymptotic behavior of edge-reinforced random walks.*

The Annals of Probability, 35 (2007) 1, 115-140. Article - with H. Matzinger:

*Retrieving random media.*

Probability Theory and Related Fields, 136 (2006), 3, 469-507. Article - with P. Diaconis:

*Bayesian analysis for reversible Markov chains.*

The Annals of Statistics, 34 (2006), 3, 1270-1292. Article - with F. Merkl:

*Linearly edge-reinforced random walks.*

Dynamics and Stochastics: Festschrift in the honor of Michael Keane. IMS Lecture Notes-Monograph Series Vol. 48 (2006) 66-77. Article -
*On the recurrence of edge-reinforced random walk on Z x G.*

Probability Theory and Related Fields 135 (2006) 2, 216-264. Article - with H. Matzinger:

*Finding blocks and other patterns in a random coloring of Z.*

Random Structures and Algorithms 28 (2006) 1, 37-75. Article - with F. Merkl:

*Edge-reinforced random walk on a ladder.*

The Annals of Probability 33 (2005) 6, 2051-2093. Article - with T.M. Liggett:

*An Infinite Stochastic Model of Social Network Formation.*

Stochastic Processes and their Applications 113 (2004) 1, 65-80. Article -
*How edge-reinforced random walk arises naturally.*

Probability Theory and Related Fields 126 (2003) 2, 243-260. Article - with H. Matzinger:

*Reconstructing a piece of scenery with polynomially many observations.*

Stochastic Processes and their Applications 107 (2003) 2, 289-300. Article - with H. Matzinger:

*Reconstructing a random scenery observed with random errors along a random walk path.*

Probability Theory and Related Fields 125 (2003) 4, 539-577. Article - with Matthias Löwe and Franz Merkl:

*Moderate Deviations for longest increasing subsequences: The lower tail.*

Journal of Theoretical Probability 15 (2002), no. 4, 1031-1047. Article - with M.S. Keane:

*Tubular recurrence.*

Acta Mathematica Hungarica 97 (2002), no. 3, 207-221. Article - with M.S. Keane:

*Edge-reinforced random walk on finite graphs.*

In P. Clement, F. den Hollander, J. van Neerven, and B. de Pagter, editors, Infinite dimensional stochastic analysis, pages 217-234. Koninklijke Nederlandse Akademie van Wetenschappen, 2000. Article