I coorganised Warsaw Summer School in Probability.


I am an assistant professor in the Faculty of Mathematics, Informatics and Mechanics, University of Warsaw.  I was a post-doc at the Université de Genève working under the supervision of prof. Yvan Velenik. Further, I was a post-doc at the Prob-Lab working with dr Simon Harris and prof. Andreas Kyprianou.

My Ph.D. supervisor was prof. Tomasz Bojdecki.


My email address is: pmilos (at)


I am interested in probability. More particularly in stochastic processes, stochastic models, branching processes, limit theorems, problems arising in the mathematical physics. (e.g. surfaces models, entropic repulsion phenomenon etc).

I take interest also in machine learning and most particulary in reinforcement learning.


You can read about it in my papers. Most of them are available on arXiv.

    Last update: 20-09-16

  • Hierarchical Reinforcement Learning with Parameters (with M. Klimek and H. Michalewski), accepted to CoRL

  • Existence of a phase transition of the interchange process on the Hamming graph (with B. Sengul), submitted (pdf)

  • Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment (with B. Mallein), submitted (pdf)

  • Brownian motion and Random Walk above Quenched Random Wall (with B. Mallein), accepted to Ann. Inst. H. Poinc (pdf)

  • Branching Brownian motion with absorption and the all-time minimum of branching Brownian motion with drift (with J. Berestycki, E. Brunet and S. Harris), accepted to J. Func. Anal. (pdf)

  • Exact representation of truncated variation of Brownian motion, submitted, arXiv:1311.2415 (pdf)

  • Piracy as an ethical decision (with M. Kobus and M. Krawczyk), accepted to Inf. Econ. Pol. (with corrections)

  • The random interchange process on the hypercube (with R. Kotecky and D. Ueltschi), Elec. Comm. Prob. 21(2016), no. 4, 1-9. (pdf)

  • Delocalization of two-dimensional random surfaces with hard-core constraints (with R. Peled), Comm. Math. Phys 340(1) (2015), pp.1-46 (pdf)

  • CLT for Ornstein-Uhlenbeck branching particle system (with R. Adamczak), Elect. J. Probab. 20 (2015), pp no. 42, 1-35 (pdf)

  • Spatial CLT for the supercritical Ornstein-Uhlenbeck superprocess, accepted (with corrections) to J. Th. Prob, arXiv:1203.6661 (pdf)

  • U-statistics of Ornstein-Uhlenbeck branching particle system (with R. Adamczak), J. Th. Prob. 27 (2014), no. 4, pp. 1071-1111 (pdf)

  • On the discrete Gaussian Free Field with disordered pinning on $\mathbb{Z}^d$, $d\geq 2$ (with L. Coquille), Stoch. Proc. Appl. 123(9) (2013), pp. 3542-3559 (pdf)

  • On truncated variation, upward truncated variation and downward truncated variation for diffusions (with R. Lochowski), Stoch. Proc. Appl. 123 (2013), pp. 446-474 (pdf)

  • Inequality decomposition by population subgroups for ordinal data (with M. Kobus), J. Health Econ. (2012), 31:15-21 (pdf)

  • Occupation times of subcritical branching immigration systems with Markov motion, CLT and deviations principles, Inf. Dim. Anal. Quant. Prob. Rel. Top. (2012) Vol. 15, No. 1 (pdf)

  • Fluctuations of the occupation times for branching system starting from infinitely divisible point processes, 2011, arXiv:1001.5142 (pdf)

  • Occupation time fluctuation limits of infinite variance equilibrium branching systems, Inf. Dim. Anal. and Quant. Probab. 2009, Vol. 12. No.4, pp. 593-612 (pdf)

  • Occupation times of subcritical branching immigration system with Markov motions, Stoch. Proc. Appl. 119 (2009), pp. 3211-3237 (pdf)

  • A note on small branching fluctuation limits of catalytic superprocesses with immigration, IMPAN Preprint 689, 2008 (pdf)

  • Limit theorems for fluctuations of occupation times of branching systems, (in Polish), 2008, Ph.D. dissertation, in polish (pdf)

  • On Meritocratic Inequality Indices (with M. Kobus), Working Paper. RePEc Archive no. 10532, 2008 (pdf)

  • Occupation time fluctuations of Poisson and equilibrium branching systems in critical and large dimensions, Prob. Math. Stat. 2008, Vol. 28, Fasc. 2, pp. 235-256 (pdf)

  • Occupation time fluctuations of Poisson and equilibrium finite variance branching systems, Prob. Math. Stat. 2007, Vol. 27, Fasc. 2, pp. 181-203 (pdf)

With whom?

I have had a pleasure to collaborate with: Radek Adamczak, Julien Berestycki, Éric Brunet, Loren Coquille, Simon Harris, Rafał Łochowski, Roman Kotecký, Martyna Kobus, Bastien Mallein, Ron Peled, Batı Şengül, Daniel Ueltschi.



Math movies

A wonderful movie depicting the famous "sphere eversion".

Do you think that the Möbius transform is difficult? Not at all!

Short talk

Surprisingly many extraordinarily intelligent people give crappy talks on conferences.
Here a few hints by Richard Durrett

And some others by Agelos Georgakopoulos Clik

Tao blog

If you've never heard of Terrence Tao go here. Later read his amazing blog.


Do you know who your mathematical ancestor was. Or you would like to know that your grand-grand-...-grand supervisor was David Hilbert ...


Well, I am not a Ph.D. student any more but the Ph.D. comics still amuses me.