List of Publications
[86] B. Jahnel, C. Külske, A. Zass, Locality properties for discrete and continuum Widom--Rowlinson models in random environments. Preprint available at arXiv:2311.07146.
[85] L. Coquille, C. Kuelske, A. Le Ny Continuity of the extremal decomposition of the free state for finite-spin models on Cayley trees. Preprint available at arXiv:2310.11101.
[84] F. Henning, C. Külske, N. Schubert, Gibbs Properties of the Bernoulli field on inhomogeneous trees under the removal of isolated sites. Preprint available at arXiv:2304.03102.
[83] A. Abbondandolo, F. Henning, C. Külske, P. Majer, Infinite-volume states with irreducible localization sets for gradient models on trees. Preprint available on arXiv:2302.05398.
[82] L. Coquille, C. Külske, A. Le Ny, Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees. J. Stat. Phys. 190:71, (2023). Article PDF
[81] N. Engler, B. Jahnel, C. Külske, Gibbsianness of locally thinned random fields. Markov Process. Relat. Fields, Volume 28, pp. 185-214, (2022). Article PDF
[80] B. Jahnel, C. Külske, Gibbsianness and non-Gibbsianness for Bernoulli lattice fields under removal of isolated sites. Bernoulli 29(4), pp. 3013–3032, (2023). Article PDF
[79] F. Henning, C. Külske, Existence of gradient Gibbs measures on regular trees which are not translation invariant. Ann. Appl. Probab. 33(4), pp. 3010-3038, (2023).
[78] S. Bergmann, S. Kissel, C. Külske, Dynamical Gibbs-non-Gibbs transitions in Widom-Rowlinson models on trees. Ann. Inst. H. Poincaré Probab. Statist. 59(1), pp. 325-344, (2023) DOI: 10.1214/22-AIHP1242. Article PDF
[77] C. Külske, D. Meißner, Dynamical Gibbs-non-Gibbs transitions in the Curie-Weiss Potts model in the regime β<3. in J Stat Phys. 78 (2021)
[76] C. Külske, D. Meißner, Stable and metastable phases for the Curie-Weiss-Potts model in vector-valued fields via singularity theory. J Stat Phys 181, 968–989 (2020).
[75] F. Henning, C. Külske,
Coexistence of localized Gibbs measures and delocalized gradient Gibbs measures on trees.
Ann. Appl. Probab. 31 (5) 2284-2310 (2021)
Article PDF
[74] S. Kissel, C. Külske,
Dynamical Gibbs-non-Gibbs transitions in lattice Widom-Rowlinson models with hard-core and soft-core interactions.
Journal of Statistical Physics volume 178, pages725–762(2020)
Preprint available at arXiv:1903.09815
[73] F. Henning, C. Külske, A. Le Ny, U. A. Rozikov,
Gradient Gibbs measures for the SOS model with countable values on a Cayley tree.
Electron. J. Probab., Volume 24 (2019), paper no. 104, 23 pp.
Preprint available at arXiv:1902.04909
[72] C. Külske,
Gibbs-non Gibbs transitions in different geometries: The Widom-Rowlinson model under stochastic spin-flip dynamics
Preprint available at arXiv:1901.10347
Accepted for publication in “Statistical Mechanics of Classical and Disordered Systems”, Springer Proceedings in Mathematics and Statistics.
[71] S. Kissel, C. Külske, U. A. Rozikov, Hard-Core and Soft-Core Widom-Rowlinson models on Cayley trees
Accepted for publication in Journal of Statistical Mechanics: Theory and Experiment,
Preprint available at arXiv:1901.09258
[70] C. Cotar, B. Jahnel, C. Külske, Extremal decomposition for random Gibbs measures: From general metastates to metastates on extremal random Gibbs measures.
Electronic Communications in Probability 2018, Vol. 23,
paper no. 95, 1-12
Preprint available at arXiv:1810.07761
[69] S. Kissel, C. Külske, Dynamical Gibbs-non-Gibbs transitions in Curie-Weiss Widom-Rowlinson
models
Markov Processes Relat. Fields 25, pp. 379–413 (2019)
Preprint available at arXiv:1903.09815
Article PDF
[68] F.Henning, R.Kraaij, C.Külske, Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction: Closing the Ising gap Bernoulli Journal Vol. 25 pp. 2051-2074 (2019). Article PDF
[67] B.Jahnel, C.Külske, Gibbsian representation for point processes via hyperedge potentials
Accepted for publication in the
Journal of Theoretical Probability. Preprint available at,
arXiv:1707.05991
[66] C.Külske, P.Schriever,
Non-robust phase transitions in the generalized clock model on trees.
Journal of Statistical Physics, Volume 170, Issue 1, pp. 1–21 (2018).
Preprint available at
arXiv:1703.06920
[65] S.Dommers, C.Külske, P.Schriever,
Continuous spin models on annealed generalized random graphs.
Stochastic Processes and their Applications, Vol. 127, pp. 3719–3753 (2017).
Preprint available at arXiv:1610.08242
[64] B.Jahnel, C.Külske, The Widom-Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality.
Ann. Appl. Probab. 27 (2017), no. 6, pp. 3845–3892.
Preprint available at arXiv:1609.01328,
Article PDF
[63] C.Külske, P.Schriever, Gradient Gibbs measures and fuzzy transformations on trees.
Markov Processes Relat. Fields 23 (2017), pp. 553–590
Preprint available at
arXiv:1609.00159
[62] B.Jahnel, C.Külske, Attractor properties for irreversible and reversible interacting
particle systems.
Commun. Math. Phys. (2019) 366: 139.
Preprint available at,
arXiv:1507.01244
[61] B.Jahnel, C.Külske,
Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction.
Bernoulli Journal, Vol. 23, pp. 2808–2827 (2017).
Preprint available at
arXiv:1502.04238
[60] B.Jahnel, C.Külske, Attractor properties of non-reversible dynamics w.r.t. invariant Gibbs measures on the lattice
Markov Processes and Related Fields, Vol. 22, pp. 507-535 (2016). Preprint available at,
arXiv:1409.8193
[59] C.Külske, U.A.Rozikov, Extremality of translation-invariant phases for a three-state SOS-model on the binary tree
Journal of Statistical Physics, Vol. 160, pp. 659-680 (2015). Preprint available at,
arXiv:1411.5886
[58] B.Jahnel, C.Külske, A class of non-ergodic weak PCAs with unique invariant measure and quasi-periodic orbit
Stochastic Processes and their Applications, Vol. 125, pp. 2427-2450 (2015). Preprint available at, arXiv:1404.3314
[57] C.Cotar, C.Külske, Uniqueness of gradient Gibbs measures with disorder
Probability Theory and Related Fields, Volume 162, Issue 3-4, pp 587-635 (2015).
Preprint available at, arXiv:1405.1449
[56] G.I.Botirov, B.Jahnel, C.Külske, Phase transition and critical values of a nearest-neighbor system with uncountable local state space on Cayley trees
Mathematical Physics, Analysis and Geometry, 1385-0172, (2014)
[55] C.Külske, U.A.Rozikov, Fuzzy transformations and extremality of Gibbs measures for the Potts model on a Cayley tree
Random Struct. Alg. 50, pp. 636–678, (2017).
Preprint available at, arXiv:1403.5775
[54] B.Jahnel, C.Külske, E.Rudelli, J.Wegener, Gibbsian and non-Gibbsian properties of the generalized mean-field fuzzy Potts-model. Markov Processes and Related Fields, Volume 20, pp 601-632 (2014). Preprint available at, arXiv:1312.5229
[53] R.M.Khakimov, C.Külske, U.A.Rozikov, Description of all translation-invariant (splitting) Gibbs measures for the Potts model on a Cayley tree
Journal of Statistical Physics, Volume 156, Issue 1, pp 189-200 (2014). Preprint available at, arXiv:1310.6220
[52] B.Jahnel, C.Külske, Synchronization for discrete mean-field rotators
Electronic Journal of Probability, Volume 19, Article 14 (2014), also available at arXiv:1308.1260
[51] B.Jahnel, C.Külske, A class of nonergodic interacting particle systems with unique invariant measure
Annals of Applied Probability, Volume 24, No. 6, 2595-2643 (2014), also available at, arXiv:1208.5433v2
[50] M.Formentin, C.Külske, A.Reichenbachs, Metastates in mean-field models with random external fields generated by Markov chains
Journal of Statistical Physics, Volume 146, Number 2 (2012), also available at, arXiv:1109.4246
[49] C.Cotar, C.Külske, Existence of random gradient states
Ann.Appl.Probab. 22 No. 4, 1650-1692 (2012), also available at,
arXiv:1012.4375
[48] A.C.D.van Enter, V.Ermolaev, G.Iacobelli, C.Külske, Gibbs-non-Gibbs properties for evolving Ising models on trees
Annales de l’Institut Henri Poincaré, Volume 48, Number 3 (2012), also available at,
arXiv:1009.2952
[47] A.C.D.van Enter, C.Külske, A.A.Opoku, Discrete approximations to vector spin models
Journal of Physics A: Mathematical and Theoretical, Volume 44, Number 47 (2011), also available at,
arXiv:1104.4241
[46] S.R.Fleurke, M.Formentin, C.Külske,
Dependent particle deposition on a graph: concentration properties of the height profile
Markov Processes and Related Fields Volume 17 Number 2, 187--208 (2011),
arXiv:1003.4599
pdf
tex
[45] V.Ermolaev, C.Külske,
Low-temperature dynamics of the Curie-Weiss Model: Periodic orbits, multiple histories, and loss of Gibbsianness
Journal of Statistical Physics, Volume 141, Number 5 (2010),
also available at,
arXiv:1005.0954
[44] G.Iacobelli, C.Külske,
Metastates in finite-type mean-field models: visibility, invisibility, and random restoration of symmetry
Journal of Statistical Physics, 2010, Volume 140, Number 1, Pages 27-55 (2010), also available at
arXiv:1003.4417v1
[43] S.R.Fleurke, C.Külske,
Multilayer Parking with Screening on a Random Tree
Journal of Statistical Physics, Volume 239, number 3, May 2010, also available at
arXiv:0911.1065
[42] A.C.D.van Enter, C.Külske, A.A.Opoku, W.M.Ruszel,
Gibbs-non-Gibbs properties for n-vector lattice and mean-field models
Brazilian Journal of Probability and Statistics, Volume 24, Number 2, pp. 226-255 (2010)
also available at arXiv:0812.1751
[41] M.Formentin, C.Külske,
A symmetric entropy bound on
the non-reconstruction regime of Markov chains on Galton-Watson trees
Electronic Communications in Probability, 14, 587-596, (2009)
pdf
tex
arXiv:0903.2962
[40] S.Fleurke, C.Külske, A second row Parking Paradox
J. Stat. Phys 136, no. 2, p. 285-295. (2009)
arXiv:0811.3599
[39] M.Formentin, C.Külske
On the Purity of the
free boundary condition Potts measure on random trees
Stochastic Processes and their Applications, 119, Issue 9, 2992-3005, (2009), also available arXiv:0810.0677
[38] C.Külske,
Metastates in random spin models,
(2008), Review article for the Modern Encyclopedia or Mathematical Physics (Springer 2009)
pdf
tex
[37] C.Külske,
The Ising model in a random magnetic field,
(2008), Review article for the Modern Encyclopedia or Mathematical Physics (Springer 2009)
pdf
tex
[36] C.Külske, A.A.Opoku,
Continuous Spin Mean-Field models:
Limiting kernels and Gibbs Properties of local transforms
arXiv:0806.0802
Journal of Math. Phys. 49, 125215 (2008) (31 pages)
[35] C.Külske, A.A.Opoku,
The Posterior metric and
the Goodness of Gibbsianness
for transforms of Gibbs measures
(2007), Electronic Journal of Probability 13, 1307-1344 (2008)
pdf
tex
arXiv:0711.3764
[34] H.Dehling, S.Fleurke, C.Külske, Parking on a random tree
J. Stat. Phys 133,
no. 1, (2008), pp. 151-157.
pdf
tex
arXiv:0711.4061
[33] C.Külske, E.Orlandi,
Continuous interfaces with disorder: Even strong pinning is too weak in 2 dimensions,
Stochastic Processes and their Applications
Volume 118, Issue 11, November 2008, Pages 1973-1981
pdf
tex
arXiv:0704.0582
[32] A.C.D.van Enter, C.Külske,
Non-existence of random gradient Gibbs measures in continuous interface models in d=2,
Annals of Applied Probability 18 (2008) 109-119,
pdf
tex
arXiv:math/0611140
[31] A.C.D.van Enter, C.Külske,
Two connections between random systems
and non-Gibbsian measures,
arXiv:math-ph/0602047
Journal of Statistical Physics 126, Numbers 4-5, 1007-1024 (2007)
[30] C.Külske, A.Le Ny,
Spin-flip dynamics of the Curie-Weiss model: Loss of Gibbsianness with possibly broken symmetry,
Comm. Math. Phys. 271 (2007), no. 2, 431--454
[29] J.-R.Chazottes, P.Collet,
C.Külske, F.Redig,
Concentration inequalities for random fields via coupling.
arXiv:math/0503483
Probab. Theory Related Fields 137 (2007), no. 1-2, 201--225
[28] C.Külske, E.Orlandi,
A simple fluctuation lower bound for a disordered massless
random continuous spin model in d=2
pdf
tex
arXiv:math/0604068
Electronic
Communications in Probability 11 (2006) 200-205
[27] C.Külske, F.Redig,
Loss without recovery of Gibbsianness during diffusion
of continuous spins,
arXiv:math-ph/0409061
Probab. Theory Related Fields 135 (2006), no. 3, 428--456
[26] A.Bovier, C.Külske,
Coarse-Graining Techniques for (random) Kac Models
,
in the volume: Interacting
stochastic systems, 11-28, Springer, Berlin (2005)
pdf-file
[25] C.Külske,
How non-Gibbsianness helps a metastable Morita minimizer to provide a stable free energy,
Markov Proc.Rel.Fields 10 No. 3, 547-564 (2004)
pdf-file
[24] O.Häggström, C.Külske,
Gibbs properties of the fuzzy Potts model on trees and in mean field
,
Markov Proc.Rel.Fields 10 No. 3, 477-506 (2004)
pdf-file
[23] C.Külske, Analogues of non-Gibbsianness in joint measures of
disordered mean field models,
J.Stat.Phys. 112 Nos. 5/6, 1101-1130 (2003)
pdf-file
[22] C.Külske, Regularity properties of potentials
for joint measures of random spin systems,
Markov Proc.Rel.Fields 10 No. 1, 75-88 (2004)
pdf-file
[21] C.Külske, A.Le Ny, F.Redig,
Relative entropy and variational properties of generalized Gibbsian measures,
Ann.Probab. 32 No. 2, 1691-1726 (2004)
pdf-file
[20] C.Külske, Concentration inequalities for functions
of Gibbs fields with application to diffraction
and random Gibbs measures,
Comm.Math.Phys. 239 No. 1/2, 29-51 (2003)
pdf-file
[19] C.Külske, Universal bounds on the selfaveraging
of random diffraction measures,
Prob.Theor.Rel.Fields 126 No. 1, 29-50 (2003)
pdf-file
[18] C.Külske, Gibbs measures of disordered spin systems,
WIAS Preprint no. 653 (2001),
review article not to be published pdf-file
[17] C.Külske, On the Gibbsian nature of the
random field Kac model under Block-averaging,
J.Stat.Phys. 104 Nos. 5/6, 991-1012 (2001)
ps-file
[16] C.Külske, Weakly Gibbsian Representations for
joint measures of quenched lattice spin models,
Prob.Theor.
Rel.Fields 119 1-30 (2001)
ps-file
[15] A.C.D.van Enter, C.Külske, C.Maes,
Comment on: Critical behavior of the randomly
spin diluted 2D Ising model: A grand ensemble approach (by R. Kühn),
Phys.Rev.Lett. 84 6134 (2000)
ps-file
[14] C.Külske, (Non-) Gibbsianness and Phase Transitions
in Random Lattice Spin Models,
Markov.Proc.Rel.Fields 5 357-383 (1999)
ps-file
[13] C.Külske, Stability for a continuous SOS-interface
model in a randomly perturbed periodic potential,
WIAS Preprint no. 466 (1998)
pdf-file
[12] C.Külske, The continuous spin random field model:
Ferromagnetic ordering in d >= 3,
Rev.Math.Phys. 11 No.10, 1269-1314 (1999) ps-file
[11] C.Külske, A random energy model for size dependence:
recurrence vs. transience,
Prob.Theor.
Rel.Fields 111 57-100 (1998)
ps-file
[10] C.Külske, Metastates in Disordered Mean-Field Models II:
The Superstates,
J.Stat.Phys. 91 1/2, 155-176 (1998)
ps-file
[9] C.Külske, Limiting behavior of random Gibbs measures: metastates
in some disordered mean field
models,
in:
Mathematical aspects of spin glasses and neural networks,
Progr. Probab. 41, 151-160,
eds. A.Bovier, P.Picco, Birkhäuser Boston,
Boston (1998)
ps-file
[8] C.Külske, Metastates in Disordered Mean-Field Models:
Random Field and Hopfield Models,
J.Stat.Phys. 88 5/6 1257-1293 (1997)
ps-file
[7] A.Bovier, C.Külske, There are no nice interfaces in
$2+1$ dimensional SOS-models in random media,
J.Stat. Phys. 83, 751-759 (1996)
pdf-file
[6] C.Külske, Instability of a hierarchical
wedding cake in a random medium: A mean field result,
Proceedings of the conference ``Advanced Topics in
Applied Mathematics and Theoretical Physics: Complex Systems''
(Marseille 1994)
ps-file
[5] A.Bovier, C.Külske, A rigorous renormalization
group method for interfaces in random media,
Rev.Math.Phys 6 No.3 (1994) 413-496
preprint ps-file
[4] C.Külske, Renormierungsgruppenanalyse
zur Untersuchung der Stabilität
von Oberflächen in ungeordneten Medien,
Ph.-D. Thesis
(Ruhr-Universität Bochum, 1993)
Scanned pdf 64 MB
[3] C.Külske,
Stability of hierarchical interfaces in stochastic media,
in: Cellular Automata and cooperative systems (Les Houches 1992),
387-394, NATO Adv.Sci.Inst.Ser.C Math.Phys, 396,
Kluwer Acad. Publ., Dordrecht, 1993
[2] A.Bovier, C.Külske,
Stability of hierarchical interfaces in random media II:
The Gibbs measures,
J.Stat.Phys 73 (1993) 253-266
preprint ps-file
[1] A.Bovier, C.Külske,
Stability of hierarchical interfaces in a random field model,
J.Stat.Phys 69 (1992) 79-110
pdf-file