Publications & preprints:
[66] |
M. Biskup and H. Huang, A limit law for the maximum of subcritical DG-model on a hierarchical lattice, preprint pdf TeX arXiv |
[65] |
M. Biskup, Homogenization theory of random walks among deterministic conductances, preprint pdf TeX arXiv |
[64] |
M. Biskup, M. Pan, An invariance principle for one-dimensional random walks in degenerate dynamical random environments, Electron. J. Probab. 28 (2023), paper no. 153, 1--18 pdf TeX arXiv published |
[63] |
M. Biskup, A. Krieger, Arithmetic oscillations of the chemical distance in long-range percolation on ℤd, Ann. Applied Probability (to appear) pdf TeX arXiv |
[62] |
M. Biskup, O. Louidor, A limit law for the most favorite point of simple random walk on a regular tree, Ann. Probab. (to appear) pdf TeX arXiv |
[61] |
M. Biskup, S. Gufler, O. Louidor, Near-maxima of the two-dimensional Discrete Gaussian Free Field, Ann. Inst. Henri Poincaré (to appear) pdf TeX arXiv |
[60] |
M. Biskup, X. Chen, T. Kumagai, J. Wang, Quenched Invariance Principle for a class of random conductance models with long-range jumps, Probab. Theory Rel. Fields 180 (2021) 847--889 pdf TeX arXiv published |
[59] |
Y. Abe, M. Biskup and S. Lee, Exceptional points of discrete-time random walks in planar domains, Electron. J. Probab. 28 (2023), paper no. 137, 1--45. pdf TeX arXiv published |
[58] |
Y. Abe and M. Biskup, Exceptional points of two-dimensional random walks at multiples of the cover time, Probab. Theory Rel. Fields 183 (2022), 1--55 pdf TeX arXiv published |
[57] |
M. Biskup, An invariance principle for one-dimensional random walks among dynamical random conductances, Electron. J. Probab. 24 (2019) paper no. 87, 1--29 pdf TeX arXiv published |
[56] |
M. Biskup, Extrema of the two-dimensional Discrete Gaussian Free Field. In: M. Barlow and G. Slade (eds.): Random Graphs, Phase Transitions, and the Gaussian Free Field. SSPROB 2017. Springer Proceedings in Mathematics & Statistics, 304 (2020) 163--407. Springer, Cham. pdf TeX arXiv published |
[55] |
M. Biskup, R. Fukushima, W. König, Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials, Interdisciplinary Information Sciences 24 (2018), no. 1, 59--76 pdf TeX arXiv published |
[54] |
M. Biskup and J. Lin, Sharp asymptotic for the chemical distance in long-range percolation, Random Struct. & Alg. 55 (2019) 560--583 pdf TeX arXiv published |
[53] |
M. Biskup and P.-F. Rodriguez, Limit theory for random walks in degenerate time-dependent random environments, J. Funct. Anal. 274 (2018), no. 4, 985--1046 pdf TeX arXiv published |
[52] |
M. Biskup, O. Louidor, On intermediate level sets of two-dimensional discrete Gaussian Free Field, Ann. Inst. Henri Poincaré 55 (2019), no. 4, 1948--1987 pdf TeX arXiv published |
[51] |
M. Biskup, J. Ding, S. Goswami, Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field, Commun. Math. Phys. 373 (2020) 45--106 pdf TeX arXiv published |
[50] |
M. Biskup, W. König and R.S. dos Santos, Mass concentration and aging in the parabolic Anderson model with doubly-exponential tails, Probab. Theory Rel. Fields 171 (2018), no. 1-2, 251--331 pdf TeX arXiv published |
[49] |
M. Biskup and O. Louidor, Full extremal process, cluster law and freezing for the two-dimensional discrete Gaussian Free Field, Adv. Math. 330 (2018) 589--687 pdf TeX arXiv published |
[48] |
M. Biskup and E.B. Procaccia, Eigenvalue vs perimeter in a shape theorem for self-interacting random walks, Ann. Appl. Probab. 28 (2018), no. 1, 340--377 pdf TeX arXiv published |
[47] |
M. Biskup and E.B. Procaccia, Shapes of drums with lowest base frequency under non-isotropic perimeter constraints, Trans. Amer. Math. Soc. 372 (2019), no. 1, 71--95. pdf TeX arXiv published |
[46] |
M. Biskup and O. Louidor, Conformal symmetries in the extremal process of two-dimensional discrete Gaussian Free Field, Commun. Math. Phys. 375 (2020), no. 1, 175--235 pdf TeX arXiv published |
[45] |
M. Biskup, R. Fukushima and W. König, Eigenvalue fluctuations for lattice Anderson Hamiltonians, SIAM J. Math. Anal. 48 (2016), no. 4, 2674--2700 pdf TeX arXiv published |
[44] |
M. Biskup and W. König, Eigenvalue order statistics for random Schrödinger operators with doubly-exponential tails, Commun. Math. Phys. 341 (2016), 179--218 pdf TeX arXiv published |
[43] |
M. Biskup and T. Richthammer, Gibbs measures on permutations over one-dimensional discrete point sets, Ann. Appl. Probab. 25 (2015), no. 2, 898--929 pdf TeX arXiv published |
[42] |
M. Biskup and O. Louidor, Extreme local extrema of two-dimensional discrete Gaussian free field, Commun. Math. Phys. 345 (2016), no. 1, 271--304 pdf TeX arXiv published |
[41] |
M. Biskup, O. Louidor, E.B. Procaccia, R. Rosenthal, Isoperimetry in two-dimensional percolation, Commun. Pure Appl. Math. 68 (2015), no. 9, 1483--1531 pdf TeX arXiv published |
[40] |
M. Biskup, M. Salvi and T. Wolff, A central limit theorem for the effective conductance: Linear boundary data and small ellipticity contrasts, Commun. Math. Phys. 328 (2014), no. 2, 701--731. pdf TeX arXiv published |
[39] |
M. Biskup, O. Louidor, A. Rozinov and A. Vandenberg-Rodes, Trapping in the random conductance model, J. Statist. Phys. 150 (2013), no. 1, 66--87 pdf TeX arXiv published |
[38] |
M. Biskup, Recent progress on the Random Conductance Model, Prob. Surveys 8 (2011) 294--373 pdf TeX arXiv published |
[37] |
M. Biskup and N. Crawford, Absence of magnetism in continuous-spin systems with long-range antialigning forces, J. Statist. Phys. 144 (2011), no. 4, 731--748 pdf TeX arXiv published |
[36] |
M. Biskup and O. Boukhadra, Subdiffusive heat-kernel decay in four-dimensional i.i.d. random conductance models, J. Lond. Math. Soc. 86 (2012), no. 2, 455--481. pdf TeX arXiv published |
[35] |
M. Biskup and R. Kotecký, True nature of long-range order in a plaquette orbital model, J. Statist. Mech. 2010 (2010), no. 11, P11001. pdf TeX arXiv published |
[34] |
M. Biskup, Graph diameter in long-range percolation, Random Structures & Algorithms 39 (2011), no. 2, 210--227. pdf TeX arXiv published |
[33] |
M. Biskup and R.H. Schonmann, Metastable behavior for bootstrap percolation on regular trees, J. Statist. Phys. 136 (2009), no. 4, 667-676. pdf TeX arXiv published |
[32] |
M. Biskup and H. Spohn, Scaling limit for a class of gradient fields with non-convex potentials, Ann. Probab. 39 (2011), no. 1, 224--251. pdf TeX arXiv published |
[31] |
M. Biskup and T.M. Prescott, Functional CLT for random walk among bounded random conductances, Electron. J. Probab. 12 (2007), paper no. 49, 1323--1348. pdf TeX arXiv published |
[30] |
N. Berger, M. Biskup, C.E. Hoffman and G. Kozma, Anomalous heat-kernel decay for random walk among bounded random conductances, Ann. Inst. Henri Poincaré 274 (2008), no. 2, 374--392. pdf TeX arXiv published |
[29] |
M. Biskup, Reflection positivity and phase transitions in lattice spin models, In: R. Kotecký (ed), Methods of Contemporary Mathematical Statistical Physics, Lecture Notes in Mathematics, vol. 1970, Springer-Verlag Berlin Heidelberg, 2009, pp. 1-86. pdf arXiv published |
[28] |
M. Biskup, L. Chayes and S.A. Kivelson, On the absence of ferromagnetism in typical 2D ferromagnets, Commun. Math. Phys. 274 (2007), no. 1, 217-231. pdf TeX arXiv published |
[27] |
M. Biskup and R. Kotecký, Phase coexistence of gradient Gibbs states, Probab. Theory Rel. Fields 139 (2007), no. 1-2, 1-39. pdf TeX arXiv published |
[26] |
M. Biskup, L. Chayes and S. Starr, Quantum spin systems at positive temperature, Commun. Math. Phys. 269 (2007), no. 3, 611-657 pdf TeX arXiv published |
[25] |
M. Biskup, L. Chayes and S.A. Smith, Large-deviations/thermodynamic approach to percolation on the complete graph, Random Structures & Algorithms 31 (2007), no. 3, 354-370. pdf TeX arXiv published |
[24] |
M. Biskup and R. Kotecký, Forbidden gap argument for phase transitions proved by means of chessboard estimates, Commun. Math. Phys. 264 (2006), no. 3, 631-656. pdf TeX arXiv published |
[23] |
N. Berger and M. Biskup, Quenched invariance principle for simple random walk on percolation clusters, Probab. Theory Rel. Fields 137 (2007), no. 1-2, 83-120. pdf TeX arXiv published |
[22] |
M. Biskup, L. Chayes and N. Crawford, Mean-field driven first-order phase transitions in systems with long-range interactions, J. Statist. Phys. 122 (2006), no. 6, 1139-1193. pdf TeX arXiv published |
[21] |
K.S. Alexander, M. Biskup and L. Chayes, Colligative properties of solutions: II. Vanishing concentrations, J. Statist. Phys. 119 (2005), no. 3-4, 509-537. pdf TeX arXiv published |
[20] |
K.S. Alexander, M. Biskup and L. Chayes, Colligative properties of solutions: I. Fixed concentrations, J. Statist. Phys. 119 (2005), no. 3-4, 479-507. pdf TeX arXiv published |
[19] |
M. Biskup, L. Chayes and S.A. Kivelson, Order by disorder, without order, in a two-dimensional spin system with O(2) symmetry, Ann. Henri Poincaré 5 (2004), no. 6, 1181-1205. pdf TeX arXiv published |
[18] |
Z. Nussinov, M. Biskup, L. Chayes and J. van den Brink, Orbital order in classical models of transition-metal compounds, Europhys. Lett. 67 (2004), no. 6, 990-996. pdf TeX arXiv published |
[17] |
M. Biskup, L. Chayes and Z. Nussinov, Orbital ordering in transition-metal compounds: I. The 120-degree model, Commun. Math. Phys. 255 (2005), no. 2, 253-292. pdf TeX arXiv published |
[16] |
M. Biskup, C. Borgs, J.T. Chayes, and R. Kotecký, Partition function zeros at first-order phase transitions: Pirogov-Sinai theory, J. Statist. Phys. 116 (2004), no. 1-4, 97-155. pdf TeX arXiv published |
[15] |
M. Biskup, On the scaling of the chemical distance in long range percolation models, Ann. Probab. 32 (2004), no. 4, 2938-2977. pdf TeX arXiv published |
[14] |
M. Biskup, C. Borgs, J.T. Chayes, L.J. Kleinwaks and R. Kotecký, Partition function zeros at first-order phase transitions: A general analysis, Commun. Math. Phys. 251 (2004), no. 1, 79-131. pdf TeX arXiv published |
[13] |
M. Biskup, L. Chayes and R. Kotecký, Comment on: "Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes", Physica A 327 (2003) 589-592. pdf TeX arXiv published |
[12] |
M. Biskup, L. Chayes and R. Kotecký, A proof of the Gibbs-Thomson formula in the droplet formation regime, J. Statist. Phys. 116 (2004), no. 1-4, 175-203. pdf TeX arXiv published |
[11] |
M. Biskup, L. Chayes and R. Kotecký, Critical region for droplet formation in the two-dimensional Ising model, Commun. Math. Phys. 242 (2003), no. 1-2, 137-183. pdf TeX arXiv published |
[10] |
M. Biskup and L. Chayes, Rigorous analysis of discontinuous phase transitions via mean-field bounds, Commun. Math. Phys. 238 (2003), no. 1-2, 53-93. pdf TeX arXiv published |
[9] |
M. Biskup, Ph. Blanchard, L. Chayes, D. Gandolfo and T. Krüger, Phase transition and critical behavior in a model of organized criticality, Probab. Theory Rel. Fields. 128 (2004), no. 1, 1-41. pdf TeX arXiv published |
[8] |
M. Biskup, L. Chayes and R. Kotecký, On the formation/dissolution of equilibrium droplets, Europhys. Lett. 60 (2002), no. 1, 21-27. pdf arXiv published |
[7] |
M. Biskup and W. König, Screening effect due to heavy lower tails in one-dimensional parabolic Anderson model, J. Statist. Phys. 102 (2001), no. 5/6, 1253-1270. arXiv published |
[6] |
M. Biskup and W. König, Long-time tails in the parabolic Anderson model with bounded potential, Ann. Probab. 29 (2001), no. 2, 636-682. arXiv published |
[5] |
M. Biskup, C. Borgs, J.T. Chayes, L.J. Kleinwaks and R. Kotecký, General theory of Lee-Yang zeros in models with first-order phase transitions, Phys. Rev. Lett. 84 (2000), no. 21, 4794-4797. arXiv published |
[4] |
M. Biskup, L. Chayes and R. Kotecký, Coexistence of partially disordered/ordered phases in an extended Potts model, J. Statist. Phys. 99 (2000), no. 5/6, 1169-1206. published |
[3] |
M. Biskup, C. Borgs, J.T. Chayes and R. Kotecký, Gibbs states of graphical representations of the Potts model with external fields, J. Math. Phys. 41 (2000), no. 3, 1170-1210. published |
[2] |
M. Biskup and F. den Hollander, A heteropolymer near a linear interface, Ann. Appl. Probab. 9 (1999), no. 3, 668-687. published |
[1] |
M. Biskup, Reflection positivity of the random-cluster measure invalidated for non-integer q, J. Statist. Phys. 92 (1998), no. 3/4, 369-375. published |
Popular articles, theses & unpublished preprints
[6] |
M. Biskup, Lecture notes for the PCMI Undergraduate Summer School, preliminary version pdf |
[5] |
M. Biskup, On Three Techniques for Rigorous Proofs of First Order Phase Transitions, PhD thesis (defended on July 30, 1999 at University of Nijmegen, The Netherlands) pdf |
[5] |
M. Biskup, L. Chayes and R. Kotecký, On the continuity of the magnetization and the energy density for Potts models on two-dimensional graphs, mp-arc version (unpublished manuscript). |
[4] |
M. Biskup, P. Cejnar and R. Kotecký, Kvantové pocítace, Vesmír 76 (1997) 250--255; A popular article in Czech on quantum computing. journal HTML transcript |
[3] |
M. Biskup, P. Cejnar and R. Kotecký, Decoherence and efficiency of quantum error correction, quant-ph/9608010 (unpublished manuscript). |
[2] |
M. Biskup, On the subshifts of compact type, Master Class paper (unpublished manuscript). |
[1] |
M. Biskup, Mean-Field Theory of Diluted Potts Models, Diploma thesis (in Czech), June 1994. |
If unable to view/print the pdf files and/or unable to download the published, email biskup@math.ucla.edu.