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Random difference equations and Renewal theory for products of random matrices
where Mn and Qn are random d • d matrices respectively d-vectors and Yn also is a d-vector. Throughout we take the sequence of pairs (Mn, Q~), n >/1, independently and identically distributed. The
The critical probability of bond percolation on the square lattice equals 1/2
We prove the statement in the title of the paper.
Scaling relations for 2D-percolation
We prove that the relations 2D-percolation hold for the usual critical exponents for 2D-percolation, provided the exponents δ andv exist. Even without the last assumption various relations
A limit theorem related to a new class of self similar processes
SummaryWe study partial sums of a stationary sequence of dependent random variables of the form $$W_n = \sum\limits_1^n {\xi \left( {S_k } \right)}$$ . Here Sk=X1 + ... +Xk where the Xiare i.i.d.
A limit law for random walk in a random environment
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