• No results found

Random walks in dynamic random environments Avena, L.

N/A
N/A
Protected

Academic year: 2021

Share "Random walks in dynamic random environments Avena, L."

Copied!
4
0
0

Bezig met laden.... (Bekijk nu de volledige tekst)

Hele tekst

(1)

Random walks in dynamic random environments

Avena, L.

Citation

Avena, L. (2010, October 26). Random walks in dynamic random environments. Retrieved from https://hdl.handle.net/1887/16072

Version: Corrected Publisher’s Version

License: Licence agreement concerning inclusion of doctoral thesis in the Institutional Repository of the University of Leiden

Downloaded from: https://hdl.handle.net/1887/16072

Note: To cite this publication please use the final published version (if applicable).

(2)

Acknowledgements

The completion of my Ph.D. could not have been accomplished without the support and the help of many people. First, I would like to thank my supervisor Prof. Dr. Frank den Hollander. Frank has been a great mentor, from him I have learned a lot about mathematics, its presentation and life in the academic world. He always found the right words to encourage me when I was stuck with my research and he has been a guide even on a personal level.

I would like to acknowledge Prof. Dr. Frank Redig from whom I have also learned a lot. I really enjoyed the time we spent working together. A special thanks to Prof. Dr.

Vladas Sidoravicius for the fruitful discussions and for introducing me to the Brazilian mathematical community. I am also very grateful to Prof. Dr. Fabio Martinelli, Prof.

Dr. Elisabetta Scoppola and Dr. Pietro Caputo who instilled in me the passion for the

“random world” during my master. Moreover, they always give me a warm welcome whenever I pass by Rome. Furthermore, I would like to thank all the committee members of my Ph.D. defence for their time, remarks and attention.

When I arrived in Leiden, I was a bit sad to be the only Ph.D. student in the new probability group. Now, I am sad to leave a really friendly, cooperative and productive group of Ph.D. students: Alessio, Alex (post-doc), Feijia, Florian, Julian, Kiamars, Stefan and Renato. I wish the best for all of you.

I would also like to thank all the scientific and supporting staff of the mathematics department in Leiden who contributed to creating a nice and stimulating environment.

My old and new friends, who always gave me the chance to stop thinking about math- ematics, have been essential for my survival. The same comments and much more go to my family in Rome, Castelluccio Inferiore and Naples. Last but not least, thanks to Giulia: she had to stand and understand me more than anyone else.

Sincere thanks to all of you.

119

(3)

Curriculum Vitae

Luca Avena was born in Rome on February 13, 1981. After finishing his high school studies at Liceo Scientifico Statale Plinio Seniore in 2000 in Rome, he started his bachelor programme in mathematics at ROMATRE University. In the meantime he continued his studies of classical guitar started in a private music academy a few years before, and in 2001 he obtained a 3-year Diploma in musical theory at the Conservatorio di Musica Licino Refice (Frosinone, Italy). During his bachelor programme he spent one year in Spain through the Erasmus exchange programme, studying at the mathematics department of the University of Granada. In 2004 he obtained the bachelor degree in Rome and started the master programme, during which he became interested in Probability Theory. In 2006 he graduated (cum laude) at ROMATRE University under the supervision of Prof. Dr. Fabio Martinelli and Dr. Pietro Caputo with the master thesis “On the threshold of the random k-sat”. In the fall of 2006 he moved to The Netherlands to start a Ph.D. programme at Leiden University under the supervision of Prof. Dr. Frank den Hollander. His Ph.D. research project has been focusing on models of random walks in dynamic random environments. On November 1, 2010, he will move to Switzerland to work at the University of Z¨urich as a post-doctoral researcher under the guidance of Prof. Dr. Erwin Bolthausen.

120

(4)

Referenties

GERELATEERDE DOCUMENTEN

In Section 2.1 we define the random walk in dynamic random environment, introduce a space-time mixing property for the random environment called cone-mixing, and state our law of

4 Large deviation principle for one-dimensional RW in dynamic RE: at- tractive spin-flips and simple symmetric exclusion 67 4.1 Introduction and main

in space but Markovian in time, i.e., at each site x there is an independent copy of the same ergodic Markov chain.. Note that, in this setup, the loss of time-independence makes

In Section 2.3 we assume a stronger space-time mixing property, namely, exponential mixing, and derive a series expansion for the global speed of the random walk in powers of the

In Section 3.2.1 we show that the path of the RW Z in (2.29), together with the evolution of the RE ξ between regeneration times, can be encoded into a chain with complete

We will see in Section 4.4 that this slow-down comes from the fact that the simple symmetric exclusion process suffers “traffic jams”, i.e., long strings of occupied and vacant

Nevertheless, similarly to the one-dimensional static RE and in contrast to the fast-mixing dynamic RE, Proposition 4.4 shows that when we look at large deviation estimates for

Large deviation principle for one- dimensional random walk in dynamic random environment: attractive spin-flips and simple symmetric exclusion.. Random walk in dynamic Markovian