Publications

2024+

[87] C. Külske, N. Schubert, A-localized states for clock models on trees and their extremal decomposition into glassy states. Preprint available at arXiv:2411.10271

[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 Non-Atomicity of the extremal decomposition of the free state for finite-spin models on Cayley trees. To appear in Ann. Inst. H. Poincaré Probab. Statist. Article PDF

[84] A. Abbondandolo, F. Henning, C. Külske, P. Majer, Infinite-volume states with irreducible localization sets for gradient models on trees. J. Stat. Phys. 191:63, (2023)

2023

[83] F. Henning, C. Külske, N. Schubert, Gibbs Properties of the Bernoulli field on inhomogeneous trees under the removal of isolated sites. Markov Process. Relat. Fields 29, pp. 641-659, (2023). Article PDF

[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)

[81] 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

[80] 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)

[79] 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). Article PDF

2022

[78] N. Engler, B. Jahnel, C. Külske, Gibbsianness of locally thinned random fields. Markov Process. Relat. Fields 28, pp. 185-214, (2022). Article PDF

2021

[77] C. Külske, D. Meißner, Dynamical Gibbs-non-Gibbs transitions in the Curie-Weiss Potts model in the regime β<3. J. Stat. Phys. 184:15, (2021)

[76] F. Henning, C. Külske, Coexistence of localized Gibbs measures and delocalized gradient Gibbs measures on trees. Ann. Appl. Probab. 31 (5), pp. 2284-2310, (2021). Article PDF

[75] B. Jahnel, C. Külske, Gibbsian representation for point processes via hyperedge potentials. Journal of Theoretical Probability 34, pp. 391-417, (2021)

2020

[74] 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, pp. 968–989, (2020)

[73] S. Kissel, C. Külske, Dynamical Gibbs-non-Gibbs transitions in lattice Widom-Rowlinson models with hard-core and soft-core interactions. J. Stat. Phys. 178, pp. 725–762, (2020)

2019

[72] 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. 24 (104), pp. 1-23, (2019)

[71] C. Külske, Gibbs-non Gibbs transitions in different geometries: The Widom-Rowlinson model under stochastic spin-flip dynamics. “Statistical Mechanics of Classical and Disordered Systems”, Springer Proceedings in Mathematics and Statistics, pp. 3-19, (2019)

[70] S. Kissel, C. Külske, U. A. Rozikov, Hard-Core and Soft-Core Widom-Rowlinson models on Cayley trees. Journal of Statistical Mechanics: Theory and Experiment, (2019)

[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). 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 25 (3), pp. 2051-2074, (2019)

[67] B. Jahnel, C. Külske, Attractor properties for irreversible and reversible interacting particle systems. Commun. Math. Phys. 366: 139, (2019)

2018

[66] 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 23 (95), pp. 1-12, (2018)

[65] C. Külske, P. Schriever, Non-robust phase transitions in the generalized clock model on trees. J. Stat. Phys. 170 (1), pp. 1–21, (2018)

2017

[64] S. Dommers, C. Külske, P. Schriever, Continuous spin models on annealed generalized random graphs. Stochastic Processes and their Applications 127, pp. 3719–3753, (2017)

[63] B. Jahnel, C. Külske, The Widom-Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality. Ann. Appl. Probab. 27 (6), pp. 3845–3892, (2017)

[62] C. Külske, P. Schriever, Gradient Gibbs measures and fuzzy transformations on trees. Markov Processes Relat. Fields 23 (4), pp. 553–590, (2017). Article PDF

[61] B. Jahnel, C. Külske, Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction. Bernoulli 23 (4A), pp. 2808–2827, (2017)

[60] C. Külske, U. A. Rozikov, Fuzzy transformations and extremality of Gibbs measures for the Potts model on a Cayley tree Random Struct. Random Struct. Alg. 50, pp. 636–678, (2017)

2016

[59] B. Jahnel, C. Külske, Attractor properties of non-reversible dynamics w.r.t. invariant Gibbs measures on the lattice. Markov Processes Relat. Fields 22 (3), pp. 507-535, (2016). Article PDF

2015

[58] C. Külske, U. A. Rozikov, Extremality of translation-invariant phases for a three-state SOS-model on the binary tree. J. Stat. Phys. 160, pp. 659-680, (2015)

[57] B. Jahnel, C. Külske, A class of non-ergodic weak PCAs with unique invariant measure and quasi-periodic orbit. Stochastic Processes and their Applications 125, pp. 2427-2450, (2015)

[56] C. Cotar, C. Külske, Uniqueness of gradient Gibbs measures with disorder. Probability Theory and Related Fields 162 (3-4), pp 587-635, (2015)

2014

[55] 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, pp. 1385-0172, (2014)

[54] B. Jahnel, C. Külske, E. Rudelli, J. Wegener, Gibbsian and non-Gibbsian properties of the generalized mean-field fuzzy Potts-model. Markov Processes Relat. Fields 20 (4), pp. 601–632, (2014). Article PDF

[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. J. Stat. Phys. 156 (1), pp. 189-200, (2014)

[52] B. Jahnel, C. Külske, Synchronization for discrete mean-field rotators. Electron. J. Probab. 19 (14), (2014)

[51] B. Jahnel, C. Külske, A class of nonergodic interacting particle systems with unique invariant measure. Ann. Appl. Probab. 24 (6), pp. 2595-2643, (2014)

2012

[50] M. Formentin, C. Külske, A. Reichenbachs, Metastates in mean-field models with random external fields generated by Markov chains. J. Stat. Phys. 146 (2), (2012)

[49] C. Cotar, C. Külske, Existence of random gradient states. Ann. Appl. Probab. 22 (4), pp. 1650-1692, (2012)

[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 48 (3), (2012)

2011

[47] A. C. D. van Enter, C. Külske, A. A. Opoku, Discrete approximations to vector spin models. Journal of Physics A: Mathematical and Theoretical 44 (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 Relat. Fields 17 (2), pp. 187-208, (2011). Article PDF

2010

[45] V. Ermolaev, C. Külske, Low-temperature dynamics of the Curie-Weiss Model: Periodic orbits, multiple histories, and loss of Gibbsianness. J. Stat. Phys. 141 (5), pp. 727-756, (2010)

[44] G. Iacobelli, C. Külske, Metastates in finite-type mean-field models: visibility, invisibility, and random restoration of symmetry. J. Stat. Phys. 140 (1), pp. 27-55, (2010)

[43] S. R. Fleurke, C. Külske, Multilayer Parking with Screening on a Random Tree. J. Stat. Phys. 239 (3), pp. 417-431, (2010)

[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. Braz. J. Probab. Stat. 24 (2), pp. 226-255, (2010)

2009

[41] M. Formentin, C. Külske, A symmetric entropy bound on the non-reconstruction regime of Markov chains on Galton-Watson trees. Electron. Commun. Probab. 14, pp. 587-596, (2009)

[40] S. Fleurke, C. Külske, A second row Parking Paradox. J. Stat. Phys 136 (2), pp. 285-295, (2009)

[39] M. Formentin, C. Külske, On the Purity of the free boundary condition Potts measure on random trees. Stochastic Processes and their Applications 119 (9), pp. 2992-3005, (2009)

[38] C. Külske, Metastates in random spin models, (2008), Review article for the Modern Encyclopedia of Mathematical Physics (Springer 2009). Article PDF, tex

[37] C. Külske, The Ising model in a random magnetic field, (2008), Review article for the Modern Encyclopedia of Mathematical Physics (Springer 2009). Article PDF, tex

2008

[36] C. Külske, A. A. Opoku, Continuous Spin Mean-Field models: Limiting kernels and Gibbs Properties of local transforms. Journal of Math. Phys. 49, 125215, 31 pages, (2008), also available at, arXiv:0806.0802

[35] C. Külske, A. A. Opoku, The Posterior metric and the Goodness of Gibbsianness for transforms of Gibbs measures . Electron. J. Probab. 13, pp. 1307-1344, (2008)

[34] H. Dehling, S. Fleurke, C. Külske, Parking on a random tree. J. Stat. Phys. 133, pp. 151-157, (2008)

[33] C. Külske, E. Orlandi, Continuous interfaces with disorder: Even strong pinning is too weak in 2 dimensions. Stochastic Processes and their Applications 118 (11), pp. 1973-1981, (2008)

[32] A. C. D. van Enter, C. Külske, Non-existence of random gradient Gibbs measures in continuous interface models in d=2. Ann. Appl. Probab. 18 (1), pp. 109-119, (2008)

2007

[31] A. C. D. van Enter, C. Külske, Two connections between random systems and non-Gibbsian measures. J. Stat. Phys. 126 (4-5), pp. 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 (2), pp. 431-454, (2007)

[29] J.-R. Chazottes, P. Collet, C. Külske, F. Redig, Concentration inequalities for random fields via coupling. Probab. Theory Related Fields 137 (1-2), pp. 201-225, (2007)

2006

[28] C. Külske, E. Orlandi, A simple fluctuation lower bound for a disordered massless random continuous spin model in d=2. Electron. Commun. Probab. 11, pp. 200-205, (2006)

[27] C. Külske, F. Redig, Loss without recovery of Gibbsianness during diffusion of continuous spins. Probab. Theory Related Fields 135, pp. 428-456, (2006)

2005

[26] A. Bovier, C. Külske, Coarse-Graining Techniques for (random) Kac Models. Interacting stochastic systems, pp. 11-28, Springer, Berlin, (2005). Article PDF

2004

[25] C. Külske, How non-Gibbsianness helps a metastable Morita minimizer to provide a stable free energy. Markov Proc. Rel. Fields 10 (3), pp. 547-564, (2004). Article PDF

[24] O. Häggström, C. Külske, Gibbs properties of the fuzzy Potts model on trees and in mean field. Markov Proc. Rel. Fields 10 (3), pp. 447-506, (2004). Article PDF

[23] C. Külske, Regularity properties of potentials for joint measures of random spin systems. Markov Proc. Rel. Fields 10 (1), pp. 75-88, (2004). Article PDF

[22] C. Külske, A. Le Ny, F. Redig, Relative entropy and variational properties of generalized Gibbsian measures. Ann. Probab. 32 (2), pp. 1691-1726, (2004)

2003

[21] C. Külske, Analogues of non-Gibbsianness in joint measures of disordered mean field models. J. Stat. Phys. 112 (5/6), pp. 1101-1130, (2003)

[20] C. Külske, Concentration inequalities for functions of Gibbs fields with application to diffraction and random Gibbs measures. Comm. Math. Phys. 239 (1/2), pp. 29-51, (2003)

[19] C. Külske, Universal bounds on the selfaveraging of random diffraction measures. Prob. Theor. Rel. Fields 126 (1), pp. 29-50, (2003)

2001

[18] C. Külske, Gibbs measures of disordered spin systems. WIAS Preprint no. 653 (2001), review article not to be published. Article PDF

[17] C. Külske, On the Gibbsian nature of the random field Kac model under Block-averaging. J. Stat. Phys. 104 (5/6), pp. 991-1012, (2001)

[16] C. Külske, Weakly Gibbsian Representations for joint measures of quenched lattice spin models. Prob. Theor. Rel. Fields 119, pp. 1-30, (2001)

2000

[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 (26), 6134, (2000). Article PDF

1999

[14] C.Külske, (Non-) Gibbsianness and Phase Transitions in Random Lattice Spin Models. Markov Proc. Rel. Fields 5 (4), pp. 357-383, (1999). Preprint available at arXiv:math-ph/9904024

[13] C. Külske, The continuous spin random field model: Ferromagnetic ordering in d >= 3. Rev. Math. Phys. 11 (10), pp. 1269-1314, (1999). Preprint available at arXiv:math-ph/9806010

1998

[12] C. Külske, Stability for a continuous SOS-interface model in a randomly perturbed periodic potential. WIAS Preprint no. 466, (1998). Article PDF

[11] C. Külske, A random energy model for size dependence: recurrence vs. transience. Prob. Theor. Rel. Fields 111, pp. 57-100, (1998)

[10] C. Külske, Metastates in Disordered Mean-Field Models II: The Superstates. J. Stat. Phys. 91 (1/2), pp. 155-176, (1998)

[9] C. Külske, Limiting behavior of random Gibbs measures: metastates in some disordered mean field modelsMathematical aspects of spin glasses and neural networks, Progr. Probab. 41, pp. 151-160, eds. A. Bovier, P. Picco, Birkhäuser Boston, Boston (1998)

1997

[8] C. Külske, Metastates in Disordered Mean-Field Models: Random Field and Hopfield Models. J.Stat.Phys. 88 (5/6), pp. 1257-1293, (1997)

1996

[7] A. Bovier, C. Külske, There are no nice interfaces in $(2+1)$-dimensional SOS-models in random media. J.Stat. Phys. 83, pp. 751-759 (1996)

1994

[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).Article PDF

[5] A. Bovier, C. Külske, A rigorous renormalization group method for interfaces in random media. Rev. Math. Phys. 6 (3), pp. 413-496, (1994). Article PDF

1993

[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. Cellular Automata and cooperative systems, pp. 387-394,(Les Houches 1992), 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, pp. 253-266, (1993)

1992

[1] A. Bovier, C. Külske, Stability of hierarchical interfaces in a random field model. J. Stat. Phys. 69, pp. 79-110, (1992)