Average Percolation

Acknowledgements In the making of this thesis I experienced a lot of support and helpfulness, at this point I would like to mention the people I feel most indebted to. I want to thank Professor David Aldous from the UC Berkeley not only for accepting my request to be my supervisor during the time in California in this exchange program but also for all the effort he put into my project and the very open-hearted way he included me in his group of fellow researchers. To him, I owe the topic of this thesis and many valuable pieces of advice. In the same way, I want to thank my supervisor here at the TUM, Professor Nina Gan-tert for all the time and work she invested to answer all my questions, make helpful suggestions and explain every concept I struggled with. Her support and also her lectures , which I found important sources of knowledge in many chapters formed the final state of this thesis. I would also like to thank the international coordinators of our faculty, especially Car-ola Jumpertz, for making this exchange program happen. Her professional counselling helped me gain experiences to cherish for a lifetime. Last but not least I want to express my heartfelt gratitude towards my family who always supported me in any situation thinkable.