171 citations
- Harvard UniversityUS3 papers
- Brookhaven National LaboratoryUS2 papers
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- Indiana University BloomingtonUS2 papers
- Michigan State UniversityUS2 papers
- Purdue University West LafayetteUS2 papers
- Romanian AcademyRO2 papers
- Tata Institute of Fundamental ResearchIN2 papers
- University of ArizonaUS2 papers
- University of Illinois Urbana-ChampaignUS2 papers
- Balseiro InstituteAR1 paper
- Brown UniversityUS1 paper
7 papers · 1 filter
An Extreme-Value Analysis of the LIL for Brownian Motion
Davar Khoshnevisan, David A. Levin, Zhan Shi
We present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. Our result can be viewed as a new improvement to the LIL.
Images of the Brownian Sheet
Davar Khoshnevisan, Yimin Xiao
An N-parameter Brownian sheet in R^d maps a non-random compact set F in R^N_+ to the random compact set B(F) in \R^d. We prove two results on the image-set B(F): (1) It has positiv…
Exceptional Times and Invariance for Dynamical Random Walks
Davar Khoshnevisan, David A. Levin, Pedro J. Mendez-Hernandez
Consider a sequence {X(i,0) : i = 1, ..., n} of i.i.d. random variables. Associate to each X(i,0) an independent mean-one Poisson clock. Every time a clock rings replace that X-var…
On the shape of the ground state eigenfunction for stable processes
Rodrigo Banuelos, Tadeusz Kulczycki, Pedro J. Mendez-Hernandez
We prove that the ground state eigenfunction for symmetric stable processes of order killed upon leaving the interval is concave on . We ca…
Levy processes: Capacity and Hausdorff dimension
Davar Khoshnevisan, Yimin Xiao
We use the recently-developed multiparameter theory of additive Levy processes to establish novel connections between an arbitrary Levy process in , and a new cla…
Continuous and discontinuous phase transitions in hypergraph processes
R. W. R. Darling, D. A. Levin, J. R. Norris
Let V denote a set of N vertices. To construct a "hypergraph process", create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random…