This is a research program which intends to provide a better understanding of deep properties of random walks in the plane, and in particular Khinchin's law of the iterated logarithm. We wish to provide quantitative estimates, and not just existence theorems. Our approach is "energy based", which means that it relies upon a description in terms of propagation of energy, fundamentally different from existing approaches. The tools which are used are derived from Operator Theory and classical Analysis (in particular Chebyshev's polynomials).

The research program includes articles, usually in preprint format, but also investigation tools, usually in Excel format (VBA programming). Comments are welcome and should be sent to bernard.beauzamy@scmsa.com.

• Part 1 : Basic settings
• Part 2 : Identical Initial Fortunes
• Part 3 : Different Initial Fortunes
• Part 4 : Variable barriers
• Part 5 : Khinchin's curves