Bartosz Trojan
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Bartosz Trojan has a total of 22 co-authors. Here are the top co-authors by number of shared publications:
- Jean-Philippe Anker
Institut Denis Poisson (UMR 7013), Université d’Orléans, Université de Tours & CNRS, Orléans Cedex 2, France
6 shared publications - Bertrand Rémy
Unité de Mathématiques Pures et Appliquées (UMR 5669), École normale supérieure de Lyon, Lyon Cedex 07, France
4 shared publications - Grzegorz Świderski
Department of Mathematics, KU Leuven, Leuven, Belgium
4 shared publications - Tomasz Grzywny
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wrocław, Poland
4 shared publications - Grzegorz Świderski
Mathematical Institute, University of Wrocław, Wrocław, Poland
3 shared publications - Effie Papageorgiou
Institut fur Mathematik, Universitat Paderborn, Paderborn, Germany
2 shared publications
Latest Publications
- 2 October 2026
- Published by Springer Nature in Mathematische Annalen
- Vol. 396 (3) , 55
Construction of Brooks–Lindenstrauss kernels on affine buildings of arbitrary reduced type, with applications
- 2 October 2026
- Published by Springer Nature in Mathematische Annalen
- Vol. 396 (3) , 55
Construction of Brooks–Lindenstrauss kernels on affine buildings of arbitrary reduced type, with applications
- Open Access
- 17 April 2026
- Published by Springer Nature in Mathematische Annalen
- Vol. 395 (2) , 30
Mass functions and asymptotic behavior of caloric functions on affine buildings
We study the large-time asymptotic behavior of solutions to the discrete-time heat equation, i.e., caloric functions, on affine buildings, including those without transitive group actions. For each $$p \in [1, \infty ]$$ , we introduce a notion of a p -mass function and prove that caloric functions with initial data belonging to certain weighted- $$\ell ^1$$ spaces or to the radial $$\ell ^1$$ class, asymptotically decouple as the product of this mass function and the heat kernel. These results extend classical analogues from Euclidean spaces and symmetric spaces of non-compact type to the non-Archimedean setting, and remain valid even for exotic buildings beyond the Bruhat–Tits framework. We characterize the spatial concentration of heat kernels in p -norms and describe the geometry of associated critical regions. Our results highlight substantial differences in the asymptotic regimes depending on the value of p , and clarify the interplay between volume growth and heat diffusion.- 17 April 2026
- Published by Springer Nature in Mathematische Annalen
- Vol. 395 (2) , 30
Open AccessMass functions and asymptotic behavior of caloric functions on affine buildings
We study the large-time asymptotic behavior of solutions to the discrete-time heat equation, i.e., caloric functions, on affine buildings, including those without transitive group actions. For each $$p \in [1, \infty ]$$ , we introduce a notion of a p -mass function and prove that caloric functions with initial data belonging to certain weighted- $$\ell ^1$$ spaces or to the radial $$\ell ^1$$ class, asymptotically decouple as the product of this mass function and the heat kernel. These results extend classical analogues from Euclidean spaces and symmetric spaces of non-compact type to the non-Archimedean setting, and remain valid even for exotic buildings beyond the Bruhat–Tits framework. We characterize the spatial concentration of heat kernels in p -norms and describe the geometry of associated critical regions. Our results highlight substantial differences in the asymptotic regimes depending on the value of p , and clarify the interplay between volume growth and heat diffusion. - 10 February 2026
- Published by Elsevier in Journal of Differential Equations
- Vol. 464
Sturm–Liouville operators with periodically modulated parameters. Part I: Regular case
- 10 February 2026
- Published by Elsevier in Journal of Differential Equations
- Vol. 464
Sturm–Liouville operators with periodically modulated parameters. Part I: Regular case
- Top Cited Papers
- 3 February 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of the European Mathematical Society
- Vol. 28 (5) , 1979-2066
Martin compactifications of affine buildings
We carry out an in-depth study of Martin compactifications of affine buildings, from the viewpoint of potential theory and random walks. This work does not use any group action on buildings, although all the results are also stated within the framework of the Bruhat–Tits theory of semisimple groups over non-Archimedean local fields. This choice should allow the use of these building compactifications in intriguing geometric group theory situations, where only lattice actions are available. The resulting compactified spaces use and, at the same time, make it possible to understand geometrically the descriptions of asymptotic behavior of kernels resulting from the non-Archimedean harmonic analysis on affine buildings. Along the paper, we make explicit the most substantial differences from the case of symmetric spaces, namely absence of a group action but existence of precise asymptotics of Green kernels and, of course, no possibility of relying on standard techniques from PDEs.
- 3 February 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of the European Mathematical Society
- Vol. 28 (5) , 1979-2066
Top Cited PapersMartin compactifications of affine buildings
We carry out an in-depth study of Martin compactifications of affine buildings, from the viewpoint of potential theory and random walks. This work does not use any group action on buildings, although all the results are also stated within the framework of the Bruhat–Tits theory of semisimple groups over non-Archimedean local fields. This choice should allow the use of these building compactifications in intriguing geometric group theory situations, where only lattice actions are available. The resulting compactified spaces use and, at the same time, make it possible to understand geometrically the descriptions of asymptotic behavior of kernels resulting from the non-Archimedean harmonic analysis on affine buildings. Along the paper, we make explicit the most substantial differences from the case of symmetric spaces, namely absence of a group action but existence of precise asymptotics of Green kernels and, of course, no possibility of relying on standard techniques from PDEs.
- Open Access
- 13 August 2025
- Published by Elsevier in Journal of Functional Analysis
- Vol. 289 (12)
Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients
- 13 August 2025
- Published by Elsevier in Journal of Functional Analysis
- Vol. 289 (12)
Open AccessAsymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients
- Open Access
Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings
We study the large-time asymptotic behavior of solutions to the discrete-time heat equation, i.e., caloric functions, on affine buildings, including those without transitive group actions. For each $p \in [1, \infty]$, we introduce a notion of a $p$-mass function and prove that caloric functions with initial data belonging to certain weighted-$\ell^1$ spaces or to the radial $\ell^1$ class, asymptotically decouple as the product of this mass function and the heat kernel. These results extend classical analogues from Euclidean spaces and symmetric spaces of non-compact type to the non-Archimedean setting, and remain valid even for exotic buildings beyond the Bruhat--Tits framework. We characterize the spatial concentration of heat kernels in $p$-norms and describe the geometry of associated critical regions. Our results highlight substantial differences in the asymptotic regimes depending on the value of $p$, and clarify the interplay between volume growth and heat diffusion.Open AccessMass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings
We study the large-time asymptotic behavior of solutions to the discrete-time heat equation, i.e., caloric functions, on affine buildings, including those without transitive group actions. For each $p \in [1, \infty]$, we introduce a notion of a $p$-mass function and prove that caloric functions with initial data belonging to certain weighted-$\ell^1$ spaces or to the radial $\ell^1$ class, asymptotically decouple as the product of this mass function and the heat kernel. These results extend classical analogues from Euclidean spaces and symmetric spaces of non-compact type to the non-Archimedean setting, and remain valid even for exotic buildings beyond the Bruhat--Tits framework. We characterize the spatial concentration of heat kernels in $p$-norms and describe the geometry of associated critical regions. Our results highlight substantial differences in the asymptotic regimes depending on the value of $p$, and clarify the interplay between volume growth and heat diffusion. - 1 April 2025
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 35 (4)
Partial versus total resetting for Lévy flights in d dimensions: Similarities and discrepancies
While stochastic resetting (or total resetting) is a less young and more established concept in stochastic processes, partial stochastic resetting (PSR) is a relatively new field. PSR means that, at random moments in time, a stochastic process gets multiplied by a factor between 0 and 1, thus approaching but not reaching the resetting position. In this paper, we present new results on PSR highlighting the main similarities and discrepancies with total resetting. Specifically, we consider both symmetric α-stable Lévy processes (Lévy flights) and Brownian motion with PSR in arbitrary d dimensions. We derive explicit expressions for the propagator and its stationary measure and discuss in detail their asymptotic behavior. Interestingly, while approaching to stationarity, a dynamical phase transition occurs for the Brownian motion, but not for Lévy flights. We also analyze the behavior of the process around the resetting position and find significant differences between PSR and total resetting.
- 1 April 2025
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 35 (4)
Partial versus total resetting for Lévy flights in d dimensions: Similarities and discrepancies
While stochastic resetting (or total resetting) is a less young and more established concept in stochastic processes, partial stochastic resetting (PSR) is a relatively new field. PSR means that, at random moments in time, a stochastic process gets multiplied by a factor between 0 and 1, thus approaching but not reaching the resetting position. In this paper, we present new results on PSR highlighting the main similarities and discrepancies with total resetting. Specifically, we consider both symmetric α-stable Lévy processes (Lévy flights) and Brownian motion with PSR in arbitrary d dimensions. We derive explicit expressions for the propagator and its stationary measure and discuss in detail their asymptotic behavior. Interestingly, while approaching to stationarity, a dynamical phase transition occurs for the Brownian motion, but not for Lévy flights. We also analyze the behavior of the process around the resetting position and find significant differences between PSR and total resetting.
- Open Access
Stationary states for stable processes with partial resetting
We study a $d$-dimensional stochastic process $\mathbf{X}$ which arises from a Lévy process $\mathbf{Y}$ by partial resetting, that is the position of the process $\mathbf{X}$ at a Poisson moment equals $c$ times its position right before the moment, and it develops as $\mathbf{Y}$ between these two consecutive moments, $c \in (0, 1)$. We focus on $\mathbf{Y}$ being a strictly $α$-stable process with $α\in (0,2]$ having a transition density: We analyze properties of the transition density $p$ of the process $\mathbf{X}$. We establish a series representation of $p$. We prove its convergence as time goes to infinity (ergodicity), and we show that the limit $ρ_{\mathbf{Y}}$ (density of the ergodic measure) can be expressed by means of the transition density of the process $\mathbf{Y}$ starting from zero, which results in closed concise formulae for its moments. We show that the process $\mathbf{X}$ reaches a non-equilibrium stationary state. Furthermore, we check that $p$ satisfies the Fokker--Planck equation, and we confirm the harmonicity of $ρ_{\mathbf{Y}}$ with respect to the adjoint generator. In detail, we discuss the following cases: Brownian motion, isotropic and $d$-cylindrical $α$-stable processes for $α\in (0,2)$, and $α$-stable subordinator for $α\in (0,1)$. We find the asymptotic behavior of $p(t;x,y)$ as $t\to +\infty$ while $(t,y)$ stays in a certain space-time region. For Brownian motion, we discover a phase transition, that is a change of the asymptotic behavior of $p(t;0,y)$ with respect to $ρ_{\mathbf{Y}}(y)$.Open AccessStationary states for stable processes with partial resetting
We study a $d$-dimensional stochastic process $\mathbf{X}$ which arises from a Lévy process $\mathbf{Y}$ by partial resetting, that is the position of the process $\mathbf{X}$ at a Poisson moment equals $c$ times its position right before the moment, and it develops as $\mathbf{Y}$ between these two consecutive moments, $c \in (0, 1)$. We focus on $\mathbf{Y}$ being a strictly $α$-stable process with $α\in (0,2]$ having a transition density: We analyze properties of the transition density $p$ of the process $\mathbf{X}$. We establish a series representation of $p$. We prove its convergence as time goes to infinity (ergodicity), and we show that the limit $ρ_{\mathbf{Y}}$ (density of the ergodic measure) can be expressed by means of the transition density of the process $\mathbf{Y}$ starting from zero, which results in closed concise formulae for its moments. We show that the process $\mathbf{X}$ reaches a non-equilibrium stationary state. Furthermore, we check that $p$ satisfies the Fokker--Planck equation, and we confirm the harmonicity of $ρ_{\mathbf{Y}}$ with respect to the adjoint generator. In detail, we discuss the following cases: Brownian motion, isotropic and $d$-cylindrical $α$-stable processes for $α\in (0,2)$, and $α$-stable subordinator for $α\in (0,1)$. We find the asymptotic behavior of $p(t;x,y)$ as $t\to +\infty$ while $(t,y)$ stays in a certain space-time region. For Brownian motion, we discover a phase transition, that is a change of the asymptotic behavior of $p(t;0,y)$ with respect to $ρ_{\mathbf{Y}}(y)$. - 1 October 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of the European Mathematical Society
- Vol. 27 (11) , 4649-4703
Asymptotic behavior of heat kernels and Green functions on affine buildings
We compute asymptotic formulas for the transition densities p(n;x,y) of finite range isotropic random walks on affine buildings. We also describe the asymptotic behavior of the corresponding Green functions.
- 1 October 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of the European Mathematical Society
- Vol. 27 (11) , 4649-4703
Asymptotic behavior of heat kernels and Green functions on affine buildings
We compute asymptotic formulas for the transition densities p(n;x,y) of finite range isotropic random walks on affine buildings. We also describe the asymptotic behavior of the corresponding Green functions.
- 14 June 2024
- Published by Elsevier in Indagationes Mathematicae
- Vol. 36 (2) , 383-412
Sharp estimates for distinguished random walks on affine buildings of type- 14 June 2024
- Published by Elsevier in Indagationes Mathematicae
- Vol. 36 (2) , 383-412
Sharp estimates for distinguished random walks on affine buildings of type