Research

Alexandrov Theorem for nonlocal curvature, with Tomasz Grzywny, submitted, arXiv 

Stable random walks in cones, with Denis Denisov, Zbigniew Palmowski and Vitali Wachtel, submitted, arXiv 

Asymptotics and geometric flows for a class of nonlocal curvatures, with Tomasz Grzywny and Julia Lenczewska, submitted, arXiv 

Bounds on the size of the convex hull of planar Brownian motion and related inverse processes, with Hugo Panzo and Stjepan Šebek, submitted, arXiv 

• Iterated-logarithm laws for convex hulls of random walks with drift, with Nikola Sandrić, Stjepan Šebek, Andrew Wade, Transactions of the American Mathematical Society 377: 6695-6724 (2024), arXiv

• Asymptotics of non-local perimeters, with Tomasz Grzywny, Annali di Matematica Pura ed Applicata 202: 2629–2651 (2023), arXiv

Invariance principle for the capacity and the cardinality of the range of stable random walks, with Nikola Sandrić and Stjepan Šebek, Stochastic Processes and their Applications 163: 61-84 (2023), arXiv

Convex hulls of stable random walks, with Nikola Sandrić and Stjepan Šebek, Electronic Journal of Probability 27: 1-30 (2022), arXiv

Decay of harmonic functions for discrete time Feynman-Kac operators with confining potentials, with Kamil Kaleta and Mateusz Śliwiński, ALEA, Latin American Journal of Probability and Mathematical Statistics 19, 1071–1101 (2022), arXiv

Central limit theorem for the capacity of the range of stable random walks, with Nikola Sandrić and Stjepan Šebek, Stochastics, Volume 94, Issue 2, Pages: 226-247, 2022, arXiv

Limit theorems for a stable sausage, with Nikola Sandrić and Stjepan Šebek, Stochastics and Dynamics, Volume No. 21, Issue No. 07, Article No. 2150041, 2021, arXiv

Functional CLT for the range of stable random walks, with Nikola Sandrić and Stjepan Šebek, Bulletin of the Malaysian Mathematical Sciences Society, Volume 44, Issue 3, pp. 1371-1386, 2021, arXiv

Transition probability estimates for subordinate random walks, with Stjepan Šebek, Mathematische Nachrichten, Volume 294, Issue 3, pp. 518-558, 2021, arXiv

Poisson approximation related to spectra of hierarchical Laplacians, with Alexander Bendikov, Stochastics and Dynamics, Volume 20, No. 5, 2020 

On the rate of convergence in the central limit theorem for hierarchical Laplacians, with Alexander Bendikov, ESAIM: Probability and Statistics, Volume 23, 2019, arXiv

Oscillating heat kernels on ultrametric spaces, with Alexander Bendikov and Wolfgang Woess, Journal of Spectral Theory, Volume 9, Issue 1, pp. 195-226, 2019, arXiv

A note on the generalized heat content for Levy processes, with Tomasz Grzywny, Bulletin of the Korean Mathematical Society 55(5), pp. 1463-1481, 2018, arXiv

On recurrence of the multidimensional Lindley process, with Judith Kloas, Electronic Communications in Probability 23 (2018), 14 pp., arXiv

Heat content for convolution semigroups, with Tomasz Grzywny, Journal of Mathematical Analysis and Applications 446(2), pp. 1393–1414, 2017, arXiv

Asymptotic behaviour of densities of unimodal convolution semigroups, with Tomasz Grzywny and Bartosz Trojan, Transactions of the American Mathematical Society 369, pp. 5623-5644, 2017, arXiv

Limit theorems for random walks, with Alexander Bendikov and Bartosz Trojan, Stochastic Processes and their Applications 127(10): 3268-3290, 2017, arXiv

On massive sets for subordinated random walks, with Alexander Bendikov, Mathematische Nachrichten 288(8-9), p. 841–853, 2015, arXiv

Alpha-stable random walk has massive thorns, with Alexander Bendikov, Colloquium Mathematicum 138 (1), p. 105-129, 2015, arXiv

Spring School in Probability, Dubrovnik (Croatia), 23-27.04, 2012, 20-min talk: Green function asymptotic for subordinated random walk

Probabilistic Aspect of Harmonic Analysis, Będlewo (Poland), 28.04-5.05, 2012, 20-min talk: Green function asymptotic for subordinated random walk

Satellite Summer School to the 7th International Conference on Lévy Processes, Będlewo (Poland), 9-13.07, 2013, poster: Massive sets for a class of random walks on the lattice Z^d

Probabilistic Aspects of Harmonic Analysis, Będlewo (Poland), 27.04-3.05, 2014, 20-min talk: Heat kernel asymptotic for subordinated random walk

Strukturtheorie-Seminar, Graz University of Technology, 02.12.2014, Asymptotic properties of subordinated random walks

Probability and Analysis, Będlewo (Poland), 03-08.05.2015, 25-min talk, Asymptotic properties of subordinated random walks

Strukturtheorie-Seminar, Graz University of Technology, 05.11.2015, Asymptotic behaviour of transition probabilities for subordinated random walk

Probabilistic Aspects of Harmonic Analysis, Będlewo (Poland), 14-21.05.2016, 30-min talk, Oscillating heat kernels on ultrametric spaces

Austrian Stochastics Days 2016, Graz (Austria), 30.06-01.07.2016, 25-min talk, Oscillating heat kernels on ultrametric spaces

Strukturtheorie-Seminar, Graz University of Technology, 12.01.2017, Heat content asymptotics for Levy processes

AG Stochastics Seminar, TU Dresden, 18.01.2018, Heat content for Lévy processes in R^d

Stochastic Methods in Analytical and Applied Problems, University of Zagreb, 13.03.2018, Heat content and its generalization for Lévy processes in R^d

Probabilistic Aspects of Harmonic Analysis, Będlewo (Poland), 07-11.05.2018, 20-min talk, Heat content and its generalization for Lévy processes

Second Interdisciplinary and Research Alumni Symposium - Workshop Mathematics, Osaka (Japan), 05-06.09.2018, 35-min talk, A class of random perturbations of hierarchical Laplacians and statistics of their spectra

Stochastic Methods in Analytical and Applied Problems, University of Zagreb, 02.10.2018, A mini course: Isotropic Markov semigroups on ultrametric spaces

Welsh Probability Seminar, Swansea University, 10.10.2019, Seminar talk: Limit theorems for the capacity of the range of stable random walks

Strukturtheorie-Seminar, Graz University of Technology, 28.12.2019, Discrete Feynman-Kac semigroups and their applications

Seminar: Teoria prawdopodobieństwa i modelowanie stochastyczne, Wroclaw (online), 03.12.2020, Limit theorems for a stable sausage

Probability and Analysis 2021 (on-line), 20-min talk, Discrete-time Feynman-Kac operators and estimates for the corresponding harmonic functions

Maxwell Institute Probability Seminar, Edinburgh, 07 April 2022, on-line talk: Convex hulls of stable random walks

Probability and Analysis 2022, Wroclaw, 19-23.09.2022, 15-min talk, Convex hulls of stable random walks

Nonlocal Operators and Markov Processes III, Będlewo (Poland), 20-24.03.2023, 40-min talk, Discrete Feynman-Kac evolutions with confining potentials

Durham Probability Afternoon (Durham University, UK), 06.09.2023, 40-min talk, Discrete Feynman-Kac evolutions with confining potentials

Discrete Random Structures, Będlewo (Poland), 16-20.10.2023, 40-min talk, Iterated-logarithm laws for convex hulls of random walks with drift 

Groups, Languages, and Random Walks, Cortona (Italy), 2-7 June 2024, 30-min talk, Discrete Feynman-Kac evolutions with confining potentials

Stochastic Reflection, Cambridge (UK), 5-9 August 2024, poster: Bounds on the size of the convex hull of planar Brownian motion

Stochastic Processes under Constraints, Bielefeld (Germany), 19-23.08.2024, 60-min talk, Stable random walks in cones

Programme: Stochastic systems for anomalous diffusion, Isaac Newton Institute for Mathematical Sciences, Cambridge (UK), 06.11.2024, 60-min talk, Stable random walks in cones

12th International Workshop for Young Mathematicians: Probability Theory and Statistics, Kraków (Poland), 20-26.09, 2009

International Conference on Analysis, Geometry and Probability Related to Group Actions, Zakopane (Poland), 17-24.04, 2010

6th International Conference on Levy Processes: Theory and Applications, Dresden (Germany), 26-30.07, 2010

II Summer school in Mathematics, Toruń (Poland), 23-27.08, 2010

I Conference on Insurance Mathematics and Investments, Łódź (Poland), 22-24.10, 2010

Summer Course in Mathematics-Perugia 2011, Perugia (Italy), 1.08-2.09, 2011

Spring School in Probability, Dubrovnik (Croatia), 23-270.4, 2012

Probabilistic Aspect of Harmonic Analysis, Będlewo (Poland), 28.04-5.05, 2012

Summer School 2012 on Nonlocal Operators, Bielefeld (Germany), 04-06.07, 2012

Bielefeld University (Germany), June 2013, 1 mont scholarship, German Academic Exchange Service (DAAD)

Satellite Summer School to the 7th International Conference on Lévy Processes, Będlewo (Poland), 9-13.07, 2013

Introductory school in Luminy, organized by: Indira Chatterji, Christophe Pittet and Laurent Saloff-Coste, Marseille (CIRM Luminy) (France), 6-17.01, 2014

Jumps 2014 - Worksop on jump processes, Dresden (Germany), 6-7.02, 2014

Probabilistic Aspects of Harmonic Analysis, Będlewo (Poland), 27.04-3.05, 2014

Groups, Graphs, and Random Walks, Cortona (Italy), 2-6 June, 2014

Probability and Analysis, Będlewo (Poland), 03-08.05.2015

Probabilistic Aspects of Harmonic Analysis, Będlewo (Poland), 14-21.05.2016

Final conférence of the MADACA project, Domaine de Chales (France), 20-24.06.2016

Austrian Stochastics Days 2016, Graz (Austria), 30.06-01.07.2016

8th International Conference on Lévy Processes, Angers (France), 25-29.07.2016.

Probability and Analysis, Będlewo (Poland), 15-19.05.2017

The 39th Conference on Stochastic Processes and their Applications (SPA2017), Moscow (Russia), 24-28.07.2017

Analysis and Applications. A conference in honor of Prof. Elias M. Stein, Wrocław (Poland), 04-08.09.2017 

Probabilistic Aspects of Harmonic Analysis. A conference in honor of Prof. Ewa Damek, Będlewo (Poland), 07-11.05.2018

The 40th Conference on Stochastic Processes and their Applications – SPA 2018, Gotheborg (Sweden), 11–15.06.2018 

Second Interdisciplinary and Research Alumni Symposium - Workshop Mathematics, Osaka (Japan), 05-06.09.2018

Joint meeting of the Italian Mathematical Union, the Italian Society of Industrial and Applied Mathematics and the Polish Mathematical Society, Wrocław (Poland), 17-20.09.2018

Probability and Analysis, Będlewo (Poland), 20-24.05.2019

Probability, Analysis, and Applications - Workshop on the occasion of the 60th birthday of Professors Hrvoje Šikić and Zoran Vondraček, Zagreb (Croatia), 12-14.06.2019

9th International Conference on Lêvy Processes, Samos (Greece), 15-19.07.2019

Dynamics, random media and universality of complex physical systems, Münster (Germany), 26-30.08.2019

Probability and Analysis 2021 (on-line), 24-28.05.2021

10th International Conference on Lévy Processes, Mannheim (Germany), 18-22.07.2022

Probability and Analysis 2022, Wroclaw, 19-23.09.2022

Nonlocal Operators and Markov Processes III, Będlewo (Poland), 20-24.03.2023

Discrete Random Structures, Będlewo (Poland), 16-20.10.2023

Probabilistic and Game Theoretical Interpretation of PDEs, Madrid (Spain), 19-24.11.2023

Groups, Languages, and Random Walks, Cortona (Italy), 2-7 June 2024

Stochastic Reflection, Cambridge (UK), 5-9 August 2024

Stochastic Processes under Constraints, Bielefeld (Germany), 19-23.08.2024

Geometry, occupation fields, and scaling limits, Cambridge (UK), 28.10-01.11.2024