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% sample references
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% Use this file as a template for your own input.
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% \biblstarthook{References may be \textit{cited} in the text either by number (preferred) or by author/year.\footnote{Make sure that all references from the list are cited in the text. Those not cited should be moved to a separate \textit{Further Reading} section or chapter.} If the citatiion in the text is numbered, the reference list should be arranged in ascending order. If the citation in the text is author/year, the reference list should be \textit{sorted} alphabetically and if there are several works by the same author, the following order should be used:
% \begin{enumerate}
% \item all works by the author alone, ordered chronologically by year of publication
% \item all works by the author with a coauthor, ordered alphabetically by coauthor
% \item all works by the author with several coauthors, ordered chronologically by year of publication.
% \end{enumerate}
% The \textit{styling} of references\footnote{Always use the standard abbreviation of a journal's name according to the ISSN \textit{List of Title Word Abbreviations}, see \url{http://www.issn.org/en/node/344}} depends on the subject of your book:
% \begin{itemize}
% \item The \textit{two} recommended styles for references in books on \textit{mathematical, physical, statistical and computer sciences} are depicted in ~\cite{science-contrib, science-online, science-mono, science-journal, science-DOI} and ~\cite{phys-online, phys-mono, phys-journal, phys-DOI, phys-contrib}.
% \item Examples of the most commonly used reference style in books on \textit{Psychology, Social Sciences} are~\cite{psysoc-mono, psysoc-online,psysoc-journal, psysoc-contrib, psysoc-DOI}.
% \item Examples for references in books on \textit{Humanities, Linguistics, Philosophy} are~\cite{humlinphil-journal, humlinphil-contrib, humlinphil-mono, humlinphil-online, humlinphil-DOI}.
% \item Examples of the basic Springer Nature style used in publications on a wide range of subjects such as \textit{Computer Science, Economics, Engineering, Geosciences, Life Sciences, Medicine, Biomedicine} are ~\cite{basic-contrib, basic-online, basic-journal, basic-DOI, basic-mono}. 
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\begin{thebibliography}{99.}%
% and use \bibitem to create references.
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% Use the following syntax and markup for your references if 
% the subject of your book is from the field 
% "Mathematics, Physics, Statistics, Computer Science"
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% Contribution

  \bibitem{bbjko16} G. Basile, C. Bernardin, M. Jara, T. Komorowski, S. Olla,
    \emph{Thermal conductivity in harmonic lattices with random
      collisions}, in ``Thermal transport in low dimensions: from
    statistical physics to nanoscale heat transfer'', S. Lepri ed.,
   {Lecture Notes in Physics} {921}, chapter 5,
   Springer 2016. DOI 10.10007/978-3-319-29261-8-5.
   
  \bibitem{bko19} G. Basile, T. Komorowski, S. Olla,
    \emph{Diffusive limits for a kinetic equation with a thermostatted interface},
    {Kinetic and Related Models},  AIMS, (2019), 12(5): 1185-1196,
    doi: 10.3934/krm.2019045.

  \bibitem{bos09} G. Basile, S. Olla, H. Spohn,
    \emph{Energy transport in stochastically perturbed lattice
     dynamics},
     {Arch. Rat. Mech.}, Vol. 195, no. 1, 171-203, 2009.
     DOI 10.1007/s00205-008-0205-6.

     
\bibitem{jko09} M. Jara, T. Komorowski, S. Olla,
  \emph{A limit theorem for an additive functionals of Markov
      chains},
    {Annals of Applied Probability}, Vol. 19, No. 6,
    2270-2300, 2009. DOI: 10.1214/09-AAP610 

     
    \bibitem{jko15} M. Jara, T. Komorowski, S. Olla,
    \emph{Superdiffusion of Energy in a system of harmonic
     oscillators with noise},
 {Commun. Math. Phys.}, {339}, 407--453 (2015), 
 DOI 10.1007/s00220-015-2417-6
 
\bibitem{GR}  Gradshteyn, I. S.; Ryzhik, I. M. {\em Table of integrals, series, and products. }Transl. from the Russian. Translation edited and with a preface by A. Jeffrey and D. Zwillinger. 
Seventh edition. Elsevier/Academic Press, Amsterdam, 2007.
 
 
\bibitem{kors18} T. Komorowski, S. Olla, L. Ryzhik, H Spohn
    \emph{High frequency limit for a chain of harmonic oscillators
      with a point Langevin thermostat.},
    {Arch. Rational Mech. An.}, 237, 497--543 (2020). 
https://doi.org/10.1007/s00205-020-01513-7.

  
\bibitem{kor19} T. Komorowski, S. Olla, L. Ryzhik,
  \emph{Fractional Diffusion limit for a kinetic equation with an interface},
 {Annals of Probability},
  Vol. 48, No. 5, 2290–2322, (2020),
https://doi.org/10.1214/20-AOP1423


\bibitem{ko19} T. Komorowski, S. Olla,
  \emph{Kinetic limit for a chain of harmonic oscillators
    with a point Langevin thermostat},
  {J.Funct.Anal.},
  279, n.12, 108764, (2020),
  https://doi.org/10.1016/j.jfa.2020.108764

\bibitem{koP} T. Komorowski, S. Olla, \emph{In preparation.}
  
\bibitem{koosis} Koosis, P., {\em Introduction to $H^p$ spaces.}
  Cambridge Univ. Press, 1980.


\bibitem{kw}  Kwa\'{s}nicki, M. {\em Ten equivalent definitions of the fractional Laplace operator.} Fract. Calc. Appl. Anal. 20 (2017), no. 1, 7�51.


\bibitem{LLP}  Lepri, S., Livi, R., Politi, A.:
  \emph{Thermal conduction in classical low-dimensional lattices.}
  Phys. Rep. 377, 1 -- 80 (2003)

  
% \bibitem{LLP}  S. Lepri, R. Livi, and A. Politi, {\em Heat Transport in Low
%   Dimensions:  Introduction and Phenomenology.}
% in ``Thermal transport in low dimensions: from
%     statistical physics to nanoscale heat transfer'', S. Lepri ed.,
%    {Lecture Notes in Physics} {921}, chapter 1,
%    Springer 2016. DOI 10.10007/978-3-319-29261-8-5.


\bibitem{RLL}  Rieder, Z., Lebowitz, J.L., Lieb, E.: Properties of harmonic crystal in a stationary non- 616 equilibrium state. J. Math. Phys. 8, 1073--1078 (1967)
  
\bibitem{spohn06} Spohn, H., \emph{The phonon Boltzmann equation,
    properties and link to weakly anharmonic lattice dynamics},
  {J. Stat. Phys.} 124, no.2-4, 1041-1104 (2006).
\bigskip

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