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Our main results, Theorems 1 and 2 below, determine all counting GFs of these two forms and give a unified combinatorial interpretation for them in terms of colored lattice paths..
Circular cylinder; laminar flow; conducting dusty fluid; velocity of dust phase and fluid phase; skin friction; periodic motion; impulsive motion; transition motion; motion for a
We show that there exist two canonical cut-and-project schemes associated with the β -numeration, allowing to lift up the β -integers to some points of the lattice Z m ( m = degree of
It has been shown that certain types of random walks in random potentials and Brownian motion in Poissonian potentials undergo a phase transition from sub-ballistic to ballistic
Keywords: supercitical percolation; exponential decay; renormalization; isoperimetric profile; anchored isoperimetry; random walk on percolation clusters; heat kernel decay; mixing
In this paper, we will compute precise asymptotics for the return probability on the lamplighter group as well as bounds for the distribution of the position of a random walk away
Keywords: Critical percolation; high-dimensional percolation; triangle condition; chemical dis- tance; intrinsic
We prove the law of large numbers for U–statistics whose underlying sequence of random variables satisfies an absolute regularity condition ( β –mixing condition) under suboptimal
