Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Harmonic functions and diffusions on treebolic spaces, trees and their boundaries.

2012/05/B/ST1/00613

Keywords:

treebolic space horocyclic product Riemannian complex hyperbolic geometry Dirichlet form diffusion process heat kernel harmonic function Dirichlet problem hypoellipticity totally disconnected set field of p-adic numbers random walk Vladimirov Laplacian spectrum spectral density

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: 8

Call: OPUS 3 - announced on 2012-03-15

Amount awarded: 150 400 PLN

Project start date (Y-m-d): 2013-01-30

Project end date (Y-m-d): 2016-01-29

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

Project status: Project settled

Equipment purchased [PL]

  1. 2 notebooki+ drukarka (2 szt.) (10 000 PLN)

Information in the final report

  • Publication in academic press/journals (8)
  • Book publications / chapters in book publications (1)
  1. On massive sets for subordinated random walks
    Authors:
    A. Bendikov, W. Cygan
    Academic press:
    Mathematische Nachrichten (rok: 2015, tom: 288(8-9), strony: 841-853), Wydawca: John Wiley and Sons
    Status:
    Published
    DOI:
    10.1002/mana.201400037 - link to the publication
  2. Isotropic Markov semigroups on ultrametric spaces
    Authors:
    A. Bendikov, A. Grigor'yan, Ch. Pittet, W. Woess
    Academic press:
    Russian Mathematical Surveys (rok: 2014, tom: 69 (4), strony: 589–680), Wydawca: London Mathematical Society
    Status:
    Published
    DOI:
    10.1070/RM2014v069n04ABEH004907 - link to the publication
  3. Brownian motion on treebolic space: escape to infinity
    Authors:
    Alexander Bendikov, Laurent Saloff-Coste, Maura Salvatori and Wolfgang Woess
    Academic press:
    Rev. Mat. Iberoam. (rok: 2015, tom: 31(3), strony: 935-976), Wydawca: Instituto de Cooperación Iberoamericana (Madrid, Spain)
    Status:
    Published
    DOI:
    10.4171/RMI/859 - link to the publication
  4. On the spectrum of the hierarchical Laplacian
    Authors:
    Alexander Bendikov, Paweł Krupski
    Academic press:
    Potential Analysis (rok: 2013, tom: -, strony: 27), Wydawca: Springer Verlag
    Status:
    Published
    DOI:
    10.1007/s11118-014-9409-6 - link to the publication
  5. Brownian motion on treebolic space: positive harmonic functions
    Authors:
    Alexander Bendikov, Laurent Saloff-Coste, Maura Salvatori, Wolfgang Woess
    Academic press:
    Annales- Institut Fourier (rok: 2016, tom: 66, strony: 1691-1731), Wydawca: Institut Fourier, Association des Annales de l'Institut Fourier
    Status:
    Published
    DOI:
    10.5802/aif.3048 - link to the publication
  6. On a class of random perturbations of the hierarchical Laplacian
    Authors:
    A. Bendikov, A. Grigor'yan, S. Molchanov, G. Samorodnitsky
    Academic press:
    Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya (rok: 2015, tom: 79, strony: 859-893), Wydawca: Russian Academy of Sciences, Academizdatcenter "Nauka"
    Status:
    Published
    DOI:
    10.1070/IM2015v079n05ABEH002764 - link to the publication
  7. Alpha-stable random walk has massive thorns
    Authors:
    A. Bendikov, W. Cygan
    Academic press:
    Colloquium Mathematicum (rok: 2015, tom: 138 (1), strony: 105-129), Wydawca: Instytut Matematyczny (Polska Akademia Nauk)
    Status:
    Published
    DOI:
    10.4064/cm138-1-7 - link to the publication
  8. Limit theorems for random walks
    Authors:
    Alexander Bendikov, Wojciech Cygan, Bartosz Trojan
    Academic press:
    Stochastic Processes and their Applications (rok: 2016, ), Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  1. Random walks on some countable groups
    Authors:
    Alexander Bendikov and Laurent Saloff-Coste
    Book:
    Groups, Graphs, and Random Walks (rok: 2017, tom: 436, strony: Chapter 2), Wydawca: Cambridge University Press; London Mathematical Society Lecture Note Series
    Status:
    Accepted for publication

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