On a linearized p-Laplace equation with rapidly oscillating coefficients
Related to a conjecture of Tom Wolff, we solve a singular Neumann problem for a linearized p-Laplace equation in the unit disk.
math.AP↗
arXiv subjects
Harri Varpanen
Publications and source records attributed to Harri Varpanen.
Geometric juggling with q-analogues
We derive a combinatorial equilibrium for bounded juggling patterns with a random, $q$-geometric throw distribution. The dynamics are analyzed via rook placements on staircase Ferrers boards, which leads to a steady-state distribution containing $q$-rook polynomial coefficients and $q$-Stirling numbers of the second kind. We show that the equilibrium probabilities of the bounded model can be uniformly approximated with the equilibrium probabilities of a corresponding unbounded model. This observation leads to new limit formulae for $q$-analogues. Keywords: juggling pattern; $q$-Stirling number of the second kind; Ferrers board; Markov process; combinatorial equilibrium
math.CO↗
Toss and Spin Juggling State Graphs
We review the state approach to toss juggling and extend the approach to spin juggling, a new concept. We give connections to current research on random juggling and describe a professional-level juggling performance that further demonstrates the state graphs and their research.
math.HO↗
The p-Laplacian with respect to measures
We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.
math.AP↗
Juggler's exclusion process
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.
math.PR↗