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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Heat kernels: construction and estimates

2016/23/B/ST1/01665

Keywords:

heat kernel Markov process infinite-dimensional torus asymptotics

Descriptors:

  • ST1_13: Probability and statistics
  • ST1_11: Partial differential equations

Panel:

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

Host institution :

Politechnika Wrocławska

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr Tomasz Grzywny 

Number of co-investigators in the project: 4

Call: OPUS 12 - announced on 2016-09-15

Amount awarded: 471 300 PLN

Project start date (Y-m-d): 2017-08-09

Project end date (Y-m-d): 2021-08-08

Project duration:: 48 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 (15 000 PLN)

Information in the final report

  • Publication in academic press/journals (13)
  1. Estimates of heat kernels of non-symmetric Levy processes
    Authors:
    Tomasz Grzywny, Karol Szczypkowski
    Academic press:
    Forum Mathematicum (rok: 2021, tom: 33 (5), strony: 1207-1236), Wydawca: WALTER DE GRUYTER GMBH
    Status:
    Published
    DOI:
    10.1515/forum-2020-0364 - link to the publication
  2. Heat kernel of fractional Laplacian with Hardy drift via desingularizing weights
    Authors:
    Damir Kinzebulatov, Yu Semenov, Karol Szczypkowski
    Academic press:
    Journal of the London Mathematical Society (rok: 2021, tom: online, strony: 14611), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1112/jlms.12486 - link to the publication
  3. Asymptotic behavior of heat kernels and Green functions on affine buildings
    Authors:
    Bartosz Trojan
    Academic press:
    Acta Mathematica , Wydawca: International Pressof Boston
    Status:
    Submitted
    DOI:
    brak - link to the publication
  4. Lévy processes: concentration function and heat kernel bounds
    Authors:
    Tomasz Grzywny, Karol Szczypkowski
    Academic press:
    Bernoulli Journal (rok: 2020, tom: 26(4), strony: 3191-3223), Wydawca: the Bernoulli Society for Mathematical Statistics and Probability
    Status:
    Published
    DOI:
    10.3150/20-BEJ1220 - link to the publication
  5. Spectral heat content for Lévy processes
    Authors:
    Tomasz Grzywny, Hyunchul Park, Renming Song
    Academic press:
    Mathematische Nachrichten (rok: 2019, tom: 292 (4), strony: 805-825), Wydawca: Wiley - V C H Verlag GmbbH & Co.
    Status:
    Published
    DOI:
    10.1002/mana.201800035 - link to the publication
  6. Heat kernels of non-symmetric Lévy-type operators
    Authors:
    Tomasz Grzywny, Karol Szczypkowski
    Academic press:
    Journal of Differential Equations (rok: 2019, tom: 267, strony: 6004 - 6064), Wydawca: Elsevier Inc.
    Status:
    Published
    DOI:
    10.1016/j.jde.2019.06.013 - link to the publication
  7. Transition densities of spectrally positive Levy processes
    Authors:
    Łukasz Leżaj
    Academic press:
    Lithuanian Mathematical Journal , Wydawca: Springer
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  8. Transition densities of subordinators of positive order
    Authors:
    Tomasz Grzywny, Łukasz Leżaj, Bartosz Trojan
    Academic press:
    Journal of the Institute of Mathematics of Jussieu (), Wydawca: CAMBRIDGE UNIV PRESS
    Status:
    Accepted for publication
    DOI:
    10.1017/S1474748021000360 - link to the publication
  9. Martin compactifications of affine buildings
    Authors:
    Bertrand Rémy, Bartosz Trojan
    Academic press:
    Acta Mathematica , Wydawca: International Press of Boston
    Status:
    Submitted
    DOI:
    brak - link to the publication
  10. Subordinated Markov processes: sharp estimates for heat kernels and the Green functions
    Authors:
    Tomasz Grzywny, Bartosz Trojan
    Academic press:
    Analysis & PDE , Wydawca: Mathematical Sciences Publishers
    Status:
    Submitted
    DOI:
    brak - link to the publication
  11. Yaglom limit for unimodal Levy processes
    Authors:
    Gavin Armstrong, Krzysztof Bogdan, Tomasz Grzywny, Łukasz Leżaj, Longmin Wang
    Academic press:
    Annals of Probability , Wydawca: Institut of Mathematical Statistics
    Status:
    Submitted
    DOI:
    brak - link to the publication
  12. Fundamental solution for super-critical non-symmetric Levy-type operators
    Authors:
    Karol Szczypkowski
    Academic press:
    Communications in Partial Differential Equations , Wydawca: Taylor&Francis
    Status:
    Submitted
    DOI:
    brak - link to the publication
  13. Regularity of fundamental solutions for Lévy-type operators
    Authors:
    Karol Szczypkowski
    Academic press:
    Annali di Matematica Pura ed Applicata , Wydawca: Springer Heidelberg
    Status:
    Submitted
    DOI:
    brak - link to the publication

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