Selected Publications and Preprints by Franz Merkl:
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with Dirk Deckert,
Detlef Dürr, and Martin Schottenloher:
Time evolution of the external field problem in QED.
Preprint (2009).
arXiv:0906.0046v1 [math-ph]
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with Silke Rolles:
Recurrence of edge-reinforced random
walk on a two-dimensional graph.
To appear in Ann. Probab. (2009).
arXiv math.PR/0703027
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with Silke Rolles:
Edge-reinforced random walk on one-dimensional periodic graphs.
Probab. Theory Related Fields Vol. 145, Nr. 3-4, 323-349 (2009).
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with A. Öry and Silke Rolles:
The 'magic formula' for linearly edge-reinforced random walks.
Statistica Neerlandica Vol. 62 Nr. 3, 345 - 363 (2008).
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with Silke Rolles:
Bounding a random environment for two-dimensional edge-reinforced random walk.
Electronic Journal of Probability,
Vol. 13, Nr. 19, 530-565 (2008).
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with Silke Rolles:
Asymptotic behavior of edge-reinforced random walk.
Ann. Probab. 35 (1), 115-140 (2007).
arXiv math.PR/0511750
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with Leila Mohammadi:
Optimal third root asymptotic bounds in the statistical estimation of thresholds.
Annals of Statistics 35 No.5, 2193-2218 (2007).
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with Silke Rolles:
A random environment for linearly edge-reinforced random walks on infinite graphs.
Probab. Theory Related Fields Vol. 138, Nr. 1-2 (2007).
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with Silke Rolles:
Linearly edge-reinforced random walks.
Dynamics and Stochastics: Festschrift in the honor of
Michael Keane.
IMS Lecture Notes-Monograph Series Vol. 48, 66-77 (2006).
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with Friedrich Götze:
Random spectral distributions.
In: Interacting stochastic systems, 181--205, Springer, Berlin, (2005).
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with
Silke Rolles:
Edge-reinforced random walk on a ladder.
Ann. Probab. 33 (2005), no. 6, 2051--2093.
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with Heinrich Matzinger
and
Matthias Löwe:
Reconstructing a Multicolor Random Scenery seen
along a Random Walk Path with Bounded Jumps.
Electronic Journal of Probability,
Vol. 9 (2004) Paper 15 (pages 436-507).
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Quenched asymptotics of the Ground State Energy
of Random Schrödinger Operators with Scaled Gibbsian Potentials.
Probab. Theory Related Fields
126, 307-338 (2003).
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with
Matthias Löwe and
Silke Rolles:
Moderate Deviations for longest increasing subsequences:
The lower tail .
Journal of Theoretical Probability 15 (2002), no. 4, 1031-1047
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with Mario Wüthrich:
Infinite volume asymptotics of the ground state energy
in a scaled Poissonian Potential.
Ann. I. Henri Poincaré - PR 38, 3 (2002) 253-284
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with
Matthias Löwe:
Moderate Deviations for longest increasing subsequences: The upper tail.
Comm. Pure Appl. Math.
54 (2001), no. 12, 1488--1520.
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with Mario Wüthrich:
Phase transition of the principal Dirichlet eigenvalue in a scaled Poissonian
potential.
Probab. Theory Related Fields
119 (2001), no. 4, 475--507.
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with Mario Wüthrich:
Annealed
Survival Asymptotics for Brownian Motion in a
Scaled Poissonian Potential.
Stochastic Processes and their Applications
96 (2001) 191--211
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Martin Zerner,
F.M.:
A zero-one law for planar random walks in random
environment.
Ann. Probab. 29 (2001), no. 4,
1716--1732.
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A Riemann Roch theorem for infinite genus Riemann surfaces.
Invent. Math. 139 (2000), no. 2,
391--437.
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Dynkin's Lemma in Measure Theory
Journal of Formalized Mathematics
Volume 12 (2000),
University of Bialystok.
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An asymptotic expansion for Bloch functions on Riemann surfaces of infinite genus and almost periodicity of the
Kadomcev-Petviashvilli flow.
Math. Phys. Anal. Geom. 2 (1999), no. 3, 245--278.
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with
Herbert Wagner:
Recurrent random walks and the absence of continuous symmetry breaking on graphs.
J. Statist. Phys. 75 (1994), no. 1-2, 153--165