Publications

TOMASZ SCHREIBER'S RESEARCH INTERESTS

  • geometric models of statistical mechanics, with special emphasis on phase transition and phase separation,
  • theory of Gibbsian point processes and stabilizing functionals,
  • polygonal Markov fi elds and their applications to image analysis,
  • limit theorems of stochastic geometry, in particular theory of large deviations in models of stochastic geometry,
  • theory of random geometric graphs, convex envelopes of point processes, random mosaics,
  • neural networks and their large-scale properties (self-organization of
    scale-free mesoscopic functional graphs, asymptotics of spectral measures).

LIST OF PUBLICATIONS

  1. SCHREIBER, T., Large deviation principle for set-valued union processes, Probab. Math. Statist., 20 (2000), 273-285.
  2. SCHREIBER, T., Statistical inference from set-valued observations, Probab. Math. Statist., 20 (2000), 223-235.
  3. SCHREIBER, T., Variance asymptotics and central limit theorems for volumes of unions of random closed sets, Adv. Appl. Probab., 34(2002), 520-539.
  4. SCHREIBER, T., Large deviation principle for spatial density of local observables from Gibbs distributions, Rep. Math. Phys., 50 (2002), 379-393.
  5. SCHREIBER, T., Limit Theorems for Certain Functionals of Unions of Random Closed Sets, Theory Probab. Appl. 47 (2003), 79-90.
  6. SCHREIBER, T., Asymptotic geometry of high-density smooth-grained Boolean models in bounded domains, Adv. Appl. Probab., 35 (2003), 913-936.
  7. SCHREIBER, T., Large deviation principle for empirical measures generated by Cox point processes, Colloq. Math., 97 (2003), 87-106.
  8. SCHREIBER, T., Surface order large deviations of phase interfaces for the continuum Widom-Rowlinson model in high density limit, Rep. Math. Phys., 53 (2004), 275-289.
  9. SCHREIBER, T., Large deviation principle for generalized quantile functions, Math. Methods Statist., 13 (2004), 472-483.
  10. ***CALKA, P., SCHREIBER, T., Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius, Ann. Probab., 33 (2005), 1625-1642.
  11. ***SCHREIBER, T., Random dynamics and thermodynamic limits for polygonal Markov fields in the plane, Adv. Appl. Probab., 37 (2005), 884-907.
  12. KLUSZCZYŃSKI, R., VAN LIESHOUT, M.N.M., SCHREIBER, T., An Algorithm for Binary Image Segmentation Using Polygonal Markov Fields, in F. Roli, S. Vitulano (Ed.), ICIAP 2005, LNCS, 3617 (2005),383-390.
  13. *** SCHREIBER, T., YUKICH, J.E., Large deviations for functionals of spatial point processes with applications to random packing and spatial graphs, Stochastic Process. Appl., 115 (2005), 1332-1356.
  14. PIĘKNIEWSKI, F. SCHREIBER, T., Phase diagrams for locally Hopfield neural networks in presence of correlated patterns, Proc. IEEE International Joint Conference on Neural Networks (IJCNN 05 (2005), Montreal, Canada), 776-781.
  15. CALKA, P., SCHREIBER, T., Large deviation probabilities for the number of vertices of random polytopes in the ball. Adv. Appl. Probab. , 38 (2006), 47-58.
  16. *** SCHREIBER, T., Dobrushin-Kotecký-Shlosman Theorem for Polygonal Markov Fields in the Plane, J. Stat. Phys., 123 (2006), 631-684.
  17. SCHREIBER, T., A Polyhedral Markov Field - pushing the Arak-Surgailis Construction into Three Dimensions. Markov Process. Related Fields, 12 (2006), 43-58.
  18. KLUSZCZYŃSKI, R., VAN LIESHOUT, M.N.M., SCHREIBER, T., Image segmentation by polygonal Markov fields, AISM, 59 (2007), 465-486.
  19. VAN LIESHOUT, M.N.M., SCHREIBER, T. Perfect Simulation for Length-interacting Polygonal Markov Fields in the Plane, Scand. J. Statist., 34 (2007), 615-625.
  20. *** SCHREIBER, T., PENROSE, M.D., YUKICH, J.E., Gaussian Limits for Multidimensional Random Sequential Packing at Saturation, Comm. Math. Phys., 272 (2007), 167-183.
  21. PIĘKNIEWSKI, F., SCHREIBER, T., Emergence of Scale-free Spike Flow Graphs in Recurrent Neural Networks, Proc. IEEE Symposium Series on Computational Intelligence - Foundations of Computational Intelligence FOCI 2007, Honolulu, Hawaii, USA, 357-362.
  22. *** SCHREIBER, T., YUKICH, J.E., Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points, Ann. Probab., 36 (2008), 363-396.
  23. BARYSHNIKOV, YU., EICHELSBACHER, P., SCHREIBER, T., YUKICH, J.E., Moderate deviations for some point measures in geometric probability, Ann. Inst. H. Poincare - Probab. Stat., 44 (2008), 422-446.
  24. *** SCHREIBER, T., Non-homogeneous Polygonal Markov Fields in the Plane: Graphical Representations and Geometry of Higher Order Correlations, J. Stat. Phys., 132 (2008), 669-705.
  25. PIĘKNIEWSKI, F., SCHREIBER, T., Spontaneous scale-free structure of spike flow graphs in recurrent neural networks, Neural Networks, 21 (2008), 1530-1536.
  26. KARŁOWSKA-PIK, J., SCHREIBER, T., Association criteria for M-infinitely-divisible and U-infinitely-divisible random sets, Probab. Math. Statist., 28 (2008), 169-178.
  27. SCHREIBER, T., Powstawanie kropli dla wielokątnych pól Markowa, Wiadomości Matematyczne, XLIV (2008), 15-22 (in Polish).
  28. *** SCHREIBER, T., Limit Theorems in Stochastic Geometry, in: New Perspectives in Stochastic Geometry, Kendall, W.S., Molchanov, I., (Eds.), Oxford Univ. Press 2010, 111-144.
  29. CZOKÓW, M., SCHREIBER, T., Adaptive Spring Systems for Shape Programming, in: L. Rutkowski et al. (Eds.), ICAISC 2010, Part II, LNAI, 6114 (2010), 420-427.
  30. EICHELSBACHER, P., SCHREIBER, T., Process level moderate deviations for stabilising functionals, ESAIM - Probab. Stat., 14 (2010), 1-15.
  31. MATUSZAK, M., SCHREIBER, T., A New Stochastic Algorithm for Strategy Optimisation in Bayesian Influence Diagrams, in: L. Rutkowski et al. (Eds.), ICAISC 2010, Part II, LNAI, 6114 (2010), 574-581.
  32. PIERSA, J., PIĘKNIEWSKI, F., SCHREIBER, T., Theoretical Model for Mesoscopic-Level Scale-Free Self-Organization of Functional Brain Networks, IEEE Trans. Neural Networks, 21 (2010), 1747-1758.
  33. *** SCHREIBER,T., Polygonal Web Representation for Higher Order Correlation Functions of Consistent Polygonal Markov Fields in the Plane, J. Stat. Phys., 140 (2010), 752-783.
  34. *** SCHREIBER, T., THÄLE, CH., Second-order properties and central limit theory for the vertex process of iteration infinitely divisible and iteration stable random tessellations in the plane, Adv. Appl. Probab., 42 (2010), 913-935.
  35. SCHREIBER, T., VAN LIESHOUT, M.N.M., Disagreement Loop and Path Creation/Annihilation Algorithms for Binary Planar Markov Fields with Applications to Image Segmentation, Scand. J. Statist., 37 (2010), 264-285.
  36. MATUSZAK, M., MIĘKISZ, J., SCHREIBER, T., Smooth Conditional Transition Paths in Dynamical Gaussian Networks, in: J. Bach and S. Edelkamp (Eds.), KI 2011, LNAI, 7006 (2011), 204-215.
  37. SCHREIBER, T., THÄLE, CH., Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations, Stochastic Process. Appl., 121 (2011), 989-1012.
  38. SCHREIBER, T., SOJA, N., Limit theory for planar Gilbert tessellations, Probab. Math. Statist., 31 (2011), 149-160.
  39. MATUSZAK, M., SCHREIBER, T., GNU Accelerated Smooth Formation Redeployment in Multiagent Environment, MASYW 2010, Instytut Podstaw Informatyki Polskiej Akademii Nauk, Warszawa, 2011, 92-100.
  40. MATUSZAK, M., SCHREIBER, T., Locally Specified Polygonal Markov Fields for Image Segmentation, in: Florack, L., Duits, R., Jongbloed, G., van Lieshout, M.-C., Davies, L., (Eds.), Mathematical Methods for Signal and Image Analysis and Representation, Springer 2012, 261-274.
  41. PIERSA, J., SCHREIBER, T., Spectra of the Spike-Flow Graphs in Geometrically Embedded Neural Networks, in: L. Rutkowski et al. (Eds.): ICAISC 2012, Part I, LNCS, 7267 (2012), 143-151.
  42. CZOKÓW, M., SCHREIBER, T., Structure Searching for Adaptive Spring Networks for Shape Programming in 3D, in: L. Rutkowski et al. (Eds.), ICAISC 2012, Part II, LNCS, 7268 (2012), 207-215.
  43. MATUSZAK, M., MIĘKISZ, J., SCHREIBER, T., Solving Ramified Optimal Transport Problem In the Bayesian Influence Diagram Framework, in: L. Rutkowski et al. (Eds.), ICAISC 2012, Part II, LNCS, 7268 (2012), 582-590.
  44. SCHREIBER, T., THÄLE, CH., Second-order theory for iteration stable tessellations, Probab. Math. Stat., 32 (2012), 281-300.
  45. CALKA, P., SCHREIBER, T., YUKICH, J.E., Brownian limits, local limits and variance asymptotics for convex hulls in the ball, Ann. Probab., 41 (2013), 50-108.
  46. SCHREIBER, T., YUKICH, J.E., Limit theorems for geometric functionals of Gibbs point processes, Ann. Inst. H. Poincare - Probab. Stat., 49 (2013), 1158-1182.
  47. SCHREIBER, T., THÄLE, CH., Limit Theorems for Iteration Stable Tessellations, Ann. Probab., 41 (2013), 2261-2278.
  48. SCHREIBER, T., THÄLE, CH., Geometry of Iteration Stable Tessellations: Connection with Poisson Hyperplanes, Bernoulli., 19 (2013), 1637-1654.
  49. SCHREIBER, T., THÄLE, CH., Shape-driven nested Markov tessellations, Stochastics, 85 (2013), 510-531.
  50. EICHELSBACHER, P., RAIČ, M., SCHREIBER, T., Moderate deviations for stabilizing functionals in geometric probability, Ann. Inst. H. Poincaré, Probab. Stat., 51 (2015), 89-128.
  51. GEORGII, H.-O., SCHREIBER, T., THÄLE, CH., Branching random tessellations with interaction: a thermodynamic view, Ann. Probab., 43 (2015), 1892-1943.
Tomasz Schreiber's Memorial Session