The power of choice in network growth (2007)
D'Souza, Raissa M., Krapivsky, Paul L., Moore, Cristopher
The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models...
Random Fibonacci sequences (2007)
Sire, Clément, Krapivsky, Paul L.
Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B -->...
Random Fibonacci Sequences (2001)
Sire, Clément, Krapivsky, Paul L.
Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B -->...
Random Fibonacci Sequences (2001)
Sire, Clément, Krapivsky, Paul L.
Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B -->...
Random Fibonacci Sequences (2001)
Sire, Clément, Krapivsky, Paul L.
Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B -->...
Island Distance in One-Dimensional Epitaxial Growth (1998)
Kallabis, Harald, Krapivsky, Paul L., Wolf, Dietrich E.
The typical island distance $\ell$ in submonlayer epitaxial growth depends on the growth conditions via an exponent $\gamma$. This exponent is known to depend on the substrate dimensionality, the...
Borderline Aggregation Kinetics in ``Dry'' and ``Wet'' Environments (1995)
Krapivsky, Paul. L., Redner, Sidney
We investigate the kinetics of constant-kernel aggregation which is augmented by either: (a) evaporation of monomers from finite-mass clusters, or (b) continuous cluster growth -- \ie, condensation....