Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Randomly perturbated Hierarchical Laplacian and Poisson statistics of its spectrum

2015/17/B/ST1/00062

Keywords:

ultrametric space hierarchical Laplacian random perturbation

Descriptors:

  • ST1_8: Analysis
  • ST1_9: Operator algebras and functional analysis
  • ST1_13: Probability and statistics

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Uniwersytet Wrocławski, Wydział Matematyki i Informatyki

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Alexander Bendikov 

Number of co-investigators in the project: 2

Call: OPUS 9 - announced on 2015-03-16

Amount awarded: 263 800 PLN

Project start date (Y-m-d): 2016-02-18

Project end date (Y-m-d): 2019-02-17

Project duration:: 36 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. Laptop (10 000 PLN)

Information in the final report

  • Publication in academic press/journals (9)
  1. On recurrence of the multidimensional Lindley process
    Authors:
    Wojciech Cygan, Judith Kloas
    Academic press:
    Electronic Communications in Probability (rok: 2018, tom: 23, strony: 14pp), Wydawca: The Institute of Mathematical Statistics
    Status:
    Published
    DOI:
    10.1214/18-ECP106 - link to the publication
  2. Heat Kernels for Isotropic-Like Markov Generators on Ultrametric Spaces: a Survey
    Authors:
    Alexander Bendikov
    Academic press:
    p-Adic Numbers, Ultrametric Analysis and Applications (rok: 2018, tom: 10, strony: 45302), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1134/S2070046618010016 - link to the publication
  3. Poisson approximation related to spectra of hierarchical Laplacians
    Authors:
    A. Bendikov, W. Cygan
    Academic press:
    Stochastics and Dynamics (rok: 2020, tom: 20(5), strony: 17pp.), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219493720500355 - link to the publication
  4. On the rate of convergence in the central limit theorem for hierarchical Laplacian
    Authors:
    Alexander Bendikov, Wojciech Cygan
    Academic press:
    ESAIM: Probability and Statistics (rok: 2019, tom: 23, strony: 68-81), Wydawca: EDP Sciences, SMAI
    Status:
    Published
    DOI:
    10.1051/ps/2018010 - link to the publication
  5. A note on the generalized heat content for Levy processes
    Authors:
    Wojciech Cygan, Tomasz Grzywny
    Academic press:
    Bulletin of the Korean Mathematical Society (rok: 2018, tom: 55(5), strony: 1463-1481), Wydawca: Korean Mathematical Society
    Status:
    Published
    DOI:
    10.4134/BKMS.b170835 - link to the publication
  6. Oscillating heat kernels on ultrametric spaces
    Authors:
    Alexander Bendikov, Wojciech Cygan and Wolfgang Woess
    Academic press:
    Journal of Spectral Theory (rok: 2019, tom: 9(1), strony: 195–226), Wydawca: EUROPEAN MATHEMATICAL SOC
    Status:
    Published
    DOI:
    10.4171/JST/245 - link to the publication
  7. Poisson statistics of eigenvalues in the hierarchical Dyson model
    Authors:
    Alexander Bendikov, Anton Braverman, John Pike
    Academic press:
    THEORY OF PROBABILITY AND ITS APPLICATIONS (rok: 2018, tom: 63(1), strony: 93-116), Wydawca: SIAM PUBLICATIONS
    Status:
    Published
    DOI:
    10.1137/S0040585X97T988939 - link to the publication
  8. Heat kernels and non-local Dirichlet forms on ultrametric spaces
    Authors:
    Alexander Bendikov, Alexander Grigor'yan, Eryan Hu, Jixaxin Hu
    Academic press:
    Annali della Scuola Normale Superiore di Pisa (rok: 2019, ), Wydawca: SCUOLA NORMALE SUPERIORE
    Status:
    Accepted for publication
    DOI:
    10.2422/2036-2145.201901_011 - link to the publication
  9. Transition probability estimates for subordinate random walks
    Authors:
    W. Cygan, S. Šebek
    Academic press:
    Mathematische Nachrichten (rok: 2019, ), Wydawca: WILEY-V C H VERLAG GMBH
    Status:
    Accepted for publication
    DOI:
    10.1002/mana.201900065 - link to the publication

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