110 citations · 146 across the 10 of their papers we have counts for
6 papers · 1 filter
Constructing processes with prescribed mixing coefficients
Leonid, Kontorovich
The rate at which dependencies between future and past observations decay in a random process may be quantified in terms of mixing coefficients. The latter in turn appear in strong…
Obtaining Measure Concentration from Markov Contraction
Leonid, Kontorovich
Concentration bounds for non-product, non-Haar measures are fairly recent: the first such result was obtained for contracting Markov chains by Marton in 1996 via the coupling metho…
Metric and Mixing Sufficient Conditions for Concentration of Measure
Leonid Kontorovich
We derive sufficient conditions for a family of metric probability spaces to have the measure concentration property. Specifically, if the sequence of pro…
Measure Concentration of Markov Tree Processes
Leonid Kontorovich
We prove an apparently novel concentration of measure result for Markov tree processes. The bound we derive reduces to the known bounds for Markov processes when the tree is a chai…
Measure Concentration of Hidden Markov Processes
Leonid Kontorovich
We prove what appears to be the first concentration of measure result for hidden Markov processes. Our bound is stated in terms of the contraction coefficients of the underlying Ma…
Concentration inequalities for dependent Random variables via the martingale method
Leonid, Kontorovich, Kavita Ramanan
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities e…