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.

Recently, I have been working in machine learning focusing in reinforcement learning. I am the PI of 500k research grant RL founded by the National Science Center. Contact me, if you are interested in Ph.D./post-doc positions.

My email address is: pmilos (at) mimuw.edu.pl

I am interested in probability. More particularly in
stochastic models, branching processes, problems arising in the mathematical physics.

Recently I focus in research i machine learning and mostly in reinforcement learning.

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

Implementation of the PPO module in open source (Tensor2Tensor framework)

Learning to Run challenge solutions: Adapting reinforcement learning methods for neuromusculoskeletal environments, NIPS 2017 competition track, (pdf)

CLT for supercritical branching processes with heavy-tailed branching law (with R. Marks), 2018, submitted (pdf)

Hierarchical Reinforcement Learning with Parameters(with M. Klimek and H. Michalewski), Proceedings of the 1st Annual Conference on Robot Learning, PMLR 78:301-313, 2017 (pdf)

Existence of a phase transition of the interchange process on the Hamming graph (with B. Sengul), accepted to Elec. J. Prob. (pdf)

Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment (with B. Mallein), accepted to Stoch. Proc. Appl. (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), J. Funct. Anal. Vol. 273, Iss 6, 2017, pp 2107-2143 (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)

Last update: 05-18

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

A wonderful movie
depicting the famous "sphere eversion".

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

Surprisingly many extraordinarily intelligent people give
crappy
talks on conferences.

Here a few hints by Richard Durrett

Click

And some others by Agelos Georgakopoulos Clik

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

Click

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

Click

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