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Abstract We discuss random interpolating sequences in weighted Dirichlet spaces $${{\mathcal{D}}}_\alpha $$, $$0\leq \alpha \leq 1$$, when the radii of the sequence points are fixed a priori and the arguments are uniformly distributed. Although conditions for deterministic interpolation in these spaces depend on capacities, which are very hard to estimate in general, we show that random interpolation is driven by surprisingly simple distribution conditions. As a consequence, we obtain a breakpoint at $$\alpha =1/2$$ in the behavior of these random interpolating sequences showing more precisely that almost sure interpolating sequences for $${{\mathcal{D}}}_\alpha $$ are exactly the almost sure separated sequences when $$0\le \alpha <1/2$$ (which includes the Hardy space $$H^2={{\mathcal{D}}}_0$$), and they are exactly the almost sure zero sequences for $${{\mathcal{D}}}_\alpha $$ when $$1/2 \leq \alpha \le 1$$ (which includes the classical Dirichlet space $${{\mathcal{D}}}={{\mathcal{D}}}_1$$).
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Ballisticity of Random walks in Random Environments on Z with Bounded Jumps
We characterize ballistic behavior for general i.i.d. random walks in random envi- ronments on Z with bounded jumps. The two characterizations we provide do not use uniform ellipticity conditions. They are natural in the sense that they both relate to formulas for the limiting speed in the nearest-neighbor case.
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- Award ID(s):
- 2153869
- PAR ID:
- 10513234
- Publisher / Repository:
- Polymat Publishing Company,
- Date Published:
- Journal Name:
- Markov processes and related fields
- Volume:
- 28
- Issue:
- 5
- ISSN:
- 1024-2953
- Page Range / eLocation ID:
- 659-671
- Subject(s) / Keyword(s):
- random walk, random environment, bounded jumps, ballisticity
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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