### NEW!

I coorganised Warsaw Summer School in Probability.

### Who?

I am an assistant professor in the   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.

### Where?

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

### What?

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

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

### How?

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

Last update: 05-18

• Phase transition for the interchange and quantum Heisenberg models on the Hamming graph (with R. Adamczak and M. Kotowski) (pdf)

• Expert-augmented actor-critic for ViZDoom and Montezumas Revenge (pdf)

• 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)

### With whom?

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.

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### 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
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And some others by Agelos Georgakopoulos Clik

### Tao blog

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

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

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

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