# T. H. Persson

## Contact Details

NameT. H. Persson |
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## Pub CategoriesMathematics - Dynamical Systems (19) Mathematics - Number Theory (5) Mathematics - Classical Analysis and ODEs (5) Mathematics - Probability (2) Mathematics - Functional Analysis (1) Physics - Accelerator Physics (1) High Energy Physics - Experiment (1) |

## Publications Authored By T. H. Persson

We prove bounds for the almost sure value of the Hausdorff dimension of the limsup set of a sequence of balls in $\mathbf{R}^d$ whose centres are independent, identically distributed random variables. The formulas obtained involve the rate of decrease of the radii of the balls and multifractal properties of the measure according to which the balls are distributed, and generalise formulas that are known to hold for particular classes of measures. Read More

**Authors:**The CLIC, CLICdp collaborations, :, M. J. Boland, U. Felzmann, P. J. Giansiracusa, T. G. Lucas, R. P. Rassool, C. Balazs, T. K. Charles, K. Afanaciev, I. Emeliantchik, A. Ignatenko, V. Makarenko, N. Shumeiko, A. Patapenka, I. Zhuk, A. C. Abusleme Hoffman, M. A. Diaz Gutierrez, M. Vogel Gonzalez, Y. Chi, X. He, G. Pei, S. Pei, G. Shu, X. Wang, J. Zhang, F. Zhao, Z. Zhou, H. Chen, Y. Gao, W. Huang, Y. P. Kuang, B. Li, Y. Li, J. Shao, J. Shi, C. Tang, X. Wu, L. Ma, Y. Han, W. Fang, Q. Gu, D. Huang, X. Huang, J. Tan, Z. Wang, Z. Zhao, T. Laštovička, U. Uggerhoj, T. N. Wistisen, A. Aabloo, K. Eimre, K. Kuppart, S. Vigonski, V. Zadin, M. Aicheler, E. Baibuz, E. Brücken, F. Djurabekova, P. Eerola, F. Garcia, E. Haeggström, K. Huitu, V. Jansson, V. Karimaki, I. Kassamakov, A. Kyritsakis, S. Lehti, A. Meriläinen, R. Montonen, T. Niinikoski, K. Nordlund, K. Österberg, M. Parekh, N. A. Törnqvist, J. Väinölä, M. Veske, W. Farabolini, A. Mollard, O. Napoly, F. Peauger, J. Plouin, P. Bambade, I. Chaikovska, R. Chehab, M. Davier, W. Kaabi, E. Kou, F. LeDiberder, R. Pöschl, D. Zerwas, B. Aimard, G. Balik, J. -P. Baud, J. -J. Blaising, L. Brunetti, M. Chefdeville, C. Drancourt, N. Geoffroy, J. Jacquemier, A. Jeremie, Y. Karyotakis, J. M. Nappa, S. Vilalte, G. Vouters, A. Bernard, I. Peric, M. Gabriel, F. Simon, M. Szalay, N. van der Kolk, T. Alexopoulos, E. N. Gazis, N. Gazis, E. Ikarios, V. Kostopoulos, S. Kourkoulis, P. D. Gupta, P. Shrivastava, H. Arfaei, M. K. Dayyani, H. Ghasem, S. S. Hajari, H. Shaker, Y. Ashkenazy, H. Abramowicz, Y. Benhammou, O. Borysov, S. Kananov, A. Levy, I. Levy, O. Rosenblat, G. D'Auria, S. Di Mitri, T. Abe, A. Aryshev, T. Higo, Y. Makida, S. Matsumoto, T. Shidara, T. Takatomi, Y. Takubo, T. Tauchi, N. Toge, K. Ueno, J. Urakawa, A. Yamamoto, M. Yamanaka, R. Raboanary, R. Hart, H. van der Graaf, G. Eigen, J. Zalieckas, E. Adli, R. Lillestøl, L. Malina, J. Pfingstner, K. N. Sjobak, W. Ahmed, M. I. Asghar, H. Hoorani, S. Bugiel, R. Dasgupta, M. Firlej, T. A. Fiutowski, M. Idzik, M. Kopec, M. Kuczynska, J. Moron, K. P. Swientek, W. Daniluk, B. Krupa, M. Kucharczyk, T. Lesiak, A. Moszczynski, B. Pawlik, P. Sopicki, T. Wojtoń, L. Zawiejski, J. Kalinowski, M. Krawczyk, A. F. Żarnecki, E. Firu, V. Ghenescu, A. T. Neagu, T. Preda, I-S. Zgura, A. Aloev, N. Azaryan, J. Budagov, M. Chizhov, M. Filippova, V. Glagolev, A. Gongadze, S. Grigoryan, D. Gudkov, V. Karjavine, M. Lyablin, A. Olyunin, A. Samochkine, A. Sapronov, G. Shirkov, V. Soldatov, A. Solodko, E. Solodko, G. Trubnikov, I. Tyapkin, V. Uzhinsky, A. Vorozhtov, E. Levichev, N. Mezentsev, P. Piminov, D. Shatilov, P. Vobly, K. Zolotarev, I. Bozovic Jelisavcic, G. Kacarevic, S. Lukic, G. Milutinovic-Dumbelovic, M. Pandurovic, U. Iriso, F. Perez, M. Pont, J. Trenado, M. Aguilar-Benitez, J. Calero, L. Garcia-Tabares, D. Gavela, J. L. Gutierrez, D. Lopez, F. Toral, D. Moya, A. Ruiz Jimeno, I. Vila, T. Argyropoulos, C. Blanch Gutierrez, M. Boronat, D. Esperante, A. Faus-Golfe, J. Fuster, N. Fuster Martinez, N. Galindo Muñoz, I. García, J. Giner Navarro, E. Ros, M. Vos, R. Brenner, T. Ekelöf, M. Jacewicz, J. Ögren, M. Olvegård, R. Ruber, V. Ziemann, D. Aguglia, N. Alipour Tehrani, A. Andersson, F. Andrianala, F. Antoniou, K. Artoos, S. Atieh, R. Ballabriga Sune, M. J. Barnes, J. Barranco Garcia, H. Bartosik, C. Belver-Aguilar, A. Benot Morell, D. R. Bett, S. Bettoni, G. Blanchot, O. Blanco Garcia, X. A. Bonnin, O. Brunner, H. Burkhardt, S. Calatroni, M. Campbell, N. Catalan Lasheras, M. Cerqueira Bastos, A. Cherif, E. Chevallay, B. Constance, R. Corsini, B. Cure, S. Curt, B. Dalena, D. Dannheim, G. De Michele, L. De Oliveira, N. Deelen, J. P. Delahaye, T. Dobers, S. Doebert, M. Draper, F. Duarte Ramos, A. Dubrovskiy, K. Elsener, J. Esberg, M. Esposito, V. Fedosseev, P. Ferracin, A. Fiergolski, K. Foraz, A. Fowler, F. Friebel, J-F. Fuchs, C. A. Fuentes Rojas, A. Gaddi, L. Garcia Fajardo, H. Garcia Morales, C. Garion, L. Gatignon, J-C. Gayde, H. Gerwig, A. N. Goldblatt, C. Grefe, A. Grudiev, F. G. Guillot-Vignot, M. L. Gutt-Mostowy, M. Hauschild, C. Hessler, J. K. Holma, E. Holzer, M. Hourican, D. Hynds, Y. Inntjore Levinsen, B. Jeanneret, E. Jensen, M. Jonker, M. Kastriotou, J. M. K. Kemppinen, R. B. Kieffer, W. Klempt, O. Kononenko, A. Korsback, E. Koukovini Platia, J. W. Kovermann, C-I. Kozsar, I. Kremastiotis, S. Kulis, A. Latina, F. Leaux, P. Lebrun, T. Lefevre, L. Linssen, X. Llopart Cudie, A. A. Maier, H. Mainaud Durand, E. Manosperti, C. Marelli, E. Marin Lacoma, R. Martin, S. Mazzoni, G. Mcmonagle, O. Mete, L. M. Mether, M. Modena, R. M. Münker, T. Muranaka, E. Nebot Del Busto, N. Nikiforou, D. Nisbet, J-M. Nonglaton, F. X. Nuiry, A. Nürnberg, M. Olvegard, J. Osborne, S. Papadopoulou, Y. Papaphilippou, A. Passarelli, M. Patecki, L. Pazdera, D. Pellegrini, K. Pepitone, E. Perez Codina, A. Perez Fontenla, T. H. B. Persson, M. Petrič, F. Pitters, S. Pittet, F. Plassard, R. Rajamak, S. Redford, Y. Renier, S. F. Rey, G. Riddone, L. Rinolfi, E. Rodriguez Castro, P. Roloff, C. Rossi, V. Rude, G. Rumolo, A. Sailer, E. Santin, D. Schlatter, H. Schmickler, D. Schulte, N. Shipman, E. Sicking, R. Simoniello, P. K. Skowronski, P. Sobrino Mompean, L. Soby, M. P. Sosin, S. Sroka, S. Stapnes, G. Sterbini, R. Ström, I. Syratchev, F. Tecker, P. A. Thonet, L. Timeo, H. Timko, R. Tomas Garcia, P. Valerio, A. L. Vamvakas, A. Vivoli, M. A. Weber, R. Wegner, M. Wendt, B. Woolley, W. Wuensch, J. Uythoven, H. Zha, P. Zisopoulos, M. Benoit, M. Vicente Barreto Pinto, M. Bopp, H. H. Braun, M. Csatari Divall, M. Dehler, T. Garvey, J. Y. Raguin, L. Rivkin, R. Zennaro, A. Aksoy, Z. Nergiz, E. Pilicer, I. Tapan, O. Yavas, V. Baturin, R. Kholodov, S. Lebedynskyi, V. Miroshnichenko, S. Mordyk, I. Profatilova, V. Storizhko, N. Watson, A. Winter, J. Goldstein, S. Green, J. S. Marshall, M. A. Thomson, B. Xu, W. A. Gillespie, R. Pan, M. A Tyrk, D. Protopopescu, A. Robson, R. Apsimon, I. Bailey, G. Burt, D. Constable, A. Dexter, S. Karimian, C. Lingwood, M. D. Buckland, G. Casse, J. Vossebeld, A. Bosco, P. Karataev, K. Kruchinin, K. Lekomtsev, L. Nevay, J. Snuverink, E. Yamakawa, V. Boisvert, S. Boogert, G. Boorman, S. Gibson, A. Lyapin, W. Shields, P. Teixeira-Dias, S. West, R. Jones, N. Joshi, R. Bodenstein, P. N. Burrows, G. B. Christian, D. Gamba, C. Perry, J. Roberts, J. A. Clarke, N. A. Collomb, S. P. Jamison, B. J. A. Shepherd, D. Walsh, M. Demarteau, J. Repond, H. Weerts, L. Xia, J. D. Wells, C. Adolphsen, T. Barklow, M. Breidenbach, N. Graf, J. Hewett, T. Markiewicz, D. McCormick, K. Moffeit, Y. Nosochkov, M. Oriunno, N. Phinney, T. Rizzo, S. Tantawi, F. Wang, J. Wang, G. White, M. Woodley

The Compact Linear Collider (CLIC) is a multi-TeV high-luminosity linear e+e- collider under development. For an optimal exploitation of its physics potential, CLIC is foreseen to be built and operated in a staged approach with three centre-of-mass energy stages ranging from a few hundred GeV up to 3 TeV. The first stage will focus on precision Standard Model physics, in particular Higgs and top-quark measurements. Read More

We consider certain parametrised families of piecewise expanding maps on the interval, and estimate and sometimes calculate the Hausdorff dimension of the set of parameters for which the orbit of a fixed point has a certain shrinking target property. This generalises several similar results for $\beta$-transformations to more general non-linear families. The proofs are based on a result by Schnellmann on typicality in parametrised families. Read More

We study parametrised families of piecewise expanding interval mappings $T_a \colon [0,1] \to [0,1]$ with absolutely continuous invariant measures $\mu_a$ and give sufficient conditions for a point $X(a)$ to be typical with respect to $(T_a, \mu_a)$ for almost all parameters $a$. This is similar to a result by D. Schnellmann, but with different assumptions. Read More

We describe a family $\phi_{\lambda}$ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems $\phi_{\lambda}$ and give some numerical evidence to suggest values of $\lambda$ for which $\phi_{\lambda}$ may be piecewise convex. Read More

Minkowski's question mark function is strictly increasing on $[0, 1]$ and hence defines a Stieltjes measure on $[0, 1]$. A problem originating from Salem in 1943, is to determine whether the Fourier series of this measure decay to zero or not. The purpose of this note is to mention that a recent result by Jordan and Sahlsten implies that the Fourier transform decays to zero with a polynomial speed. Read More

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle. Read More

For a map $T \colon [0,1] \to [0,1]$ with an invariant measure $\mu$, we study, for a $\mu$-typical $x$, the set of points $y$ such that the inequality $|T^n x - y| < r_n$ is satisfied for infinitely many $n$. We give a formula for the Hausdorff dimension of this set, under the assumption that $T$ is piecewise expanding and $\mu_\phi$ is a Gibbs measure. In some cases we also show that the set has a large intersection property. Read More

We give a sufficient condition for the Fourier dimension of a countable union of sets to equal the supremum of the Fourier dimensions of the sets in the union, and show by example that the Fourier dimension is not countably stable in general. A natural approach to finite stability of the Fourier dimension for sets would be to try to prove that the Fourier dimension for measures is finitely stable, but we give an example showing that it is not in general. We also describe some situations where the Fourier dimension for measures is stable or is stable for all but one value of some parameter. Read More

Various notions of "zooming in" on measures exist in the literature and the scenery flow is one of them. It is of interest to describe the joint asymptotics of the scenery flows generated by a measure and the measure transported by a local diffeomorphism. We give both sufficient and necessary conditions for the scenery distributions to be asymptotic and provide some examples. Read More

This note provides a generalisation of a recent result by J\"arvenp\"a\"a, J\"arvenp\"a\"a, Koivusalo, Li, and Suomala, (to appear), on the dimension of limsup-sets of random coverings of tori. The result in this note is stronger in the sense that it provides also a large intersection property of the limsup-sets, the assumptions are weaker, and it implies the result of J\"arvenp\"a\"a, J\"arvenp\"a\"a, Koivusalo, Li, and Suomala as a special case. The proof is based on a recent result by Persson and Reeve from 2013. Read More

We consider classes $\mathscr{G}^s ([0,1])$ of subsets of $[0,1]$, originally introduced by Falconer, that are closed under countable intersections, and such that every set in the class has Hausdorff dimension at least $s$. We provide a Frostman type lemma to determine if a limsup-set is in such a class. Suppose $E = \limsup E_n \subset [0,1]$, and that $\mu_n$ are probability measures with support in $E_n$. Read More

We consider the distribution of the orbits of the number 1 under the $\beta$-transformations $T_\beta$ as $\beta$ varies. Mainly, the size of the set of $\beta>1$ for which a given point can be well approximated by the orbit of 1 is measured by its Hausdorff dimension. That is, the dimension of the following set $$ E\big({\ell_n}_{n\ge 1}, x_0\big)=\Big{\beta>1: |T^n_{\beta}1-x_0|<\beta^{-\ell_n}, {for infinitely many} n\in \N\Big} $$ is determined, where $x_0$ is a given point in $[0,1]$ and ${\ell_n}_{n\ge 1}$ is a sequence of integers tending to infinity as $n\to \infty$. Read More

For $\lambda \in (1/2, 1)$ and $\alpha$, we consider sets of numbers $x$ such that for infinitely many $n$, $x$ is $2^{-\alpha n}$-close to some $\sum_{i=1}^n \omega_i \lambda^i$, where $\omega_i \in \{0,1\}$. These sets are in Falconer's intersection classes for Hausdorff dimension $s$ for some $s$ such that $- \frac{1}{\alpha} \frac{\log \lambda}{\log 2} \leq s \leq \frac{1}{\alpha}$. We show that for almost all $\lambda \in (1/2, 2/3)$, the upper bound of $s$ is optimal, but for a countable infinity of values of $\lambda$ the lower bound is the best possible result. Read More

Let $(B_{i})$ be a sequence of measurable sets in a probability space $(X,\mathcal{B}, \mu)$ such that $\sum_{n=1}^{\infty} \mu (B_{i}) = \infty$. The classical Borel-Cantelli lemma states that if the sets $B_{i}$ are independent, then $\mu (\{x \in X : x \in B_{i} \text{infinitely often (i.o. Read More

We consider the regularity of measurable solutions $\chi$ to the cohomological equation \[ \phi = \chi \circ T -\chi, \] where $(T,X,\mu)$ is a dynamical system and $\phi \colon X\rightarrow \R$ is a $C^k$ valued cocycle in the setting in which $T \colon X\rightarrow X$ is a piecewise $C^k$ Gibbs--Markov map, an affine $\beta$-transformation of the unit interval or more generally a piecewise $C^{k}$ uniformly expanding map of an interval. We show that under mild assumptions, bounded solutions $\chi$ possess $C^k$ versions. In particular we show that if $(T,X,\mu)$ is a $\beta$-transformation then $\chi$ has a $C^k$ version, thus improving a result of Pollicott et al. Read More

We study sets of nontypical points under the map $f_\beta \mapsto \beta x $ mod 1, for non-integer $\beta$ and extend our results from [F\"arm, Persson, Schmeling, 2010] in several directions. In particular we prove that sets of points whose forward orbit avoid certain Cantor sets, and set of points for which ergodic averages diverge, have large intersection properties. We observe that the technical condition $\beta>1. Read More

We consider a generalisation of the baker's transformation, consisting of a skew-product of contractions and a $\beta$-transformation. The Hausdorff dimension and Lebesgue measure of the attractor is calculated for a set of parameters with positive measure. The proofs use a new transverality lemma similar to Solomyak's [Solomyak, 1995]. Read More

We consider limit sets of some conformal iterated function systems, and introduce classes of subsets of the limit set, with the property that the classes are closed under countable intersections and all sets in the classes have large Hausdorff dimension. We show some applications in ergodic theory, Diophantine approximation and complex dynamics. Read More

We study non-invertible piecewise hyperbolic maps in the plane. The Hausdorff dimension of the attractor is calculated in terms of the Lyapunov exponents, provided that the map satisfies a transversality condition. Explicit examples of maps for which this condition holds are given. Read More

We consider some random iterated function systems on the interval and show that the invariant measure has density in $\mathcal{C}^\infty$. To prove this we use some techniques for contractions in cone metrics, applied to the transfer operator. Read More

We consider iterated function systems on the interval with random perturbation. Let $Y_\epsilon$ be uniformly distributed in $[1- \epsilon, 1 + \epsilon]$ and let $f_i \in C^{1+\alpha}$ be contractions with fixpoints $a_i$. We consider the iterated function system $\{Y_\epsilon f_i + a_i (1 - Y_\epsilon) \}_{i=1}^n$, were each of the maps are chosen with probability $p_i$. Read More

A class of piecewise affine hyperbolic maps on a bounded subset of the plane is considered. It is shown that if a map from this class is sufficiently area-expanding then almost surely this map has an absolutely continuous invariant measure. Read More