Geodesic
On some random integral operators generated by an Arratia flow
Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 8-18

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We study some properties of a random integral operator in $L_2( \mathbb{R})$ whose kernel is generated by a stationary point process related to an Arratia flow. To prove that this random operator is not bounded we estimate the rate of growth of the maximal amount of clusters in Arratia flow on intervals of unit length.
Keywords: Arratia flow, strong random operator, point process, stochastic flow. 
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     author = {A. A. Dorogovtsev and Ia. A. Korenovska and E. V. Glinyanaya},
     title = {On some random integral operators generated by an {Arratia} flow},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {8--18},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a1/}
}
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A. A. Dorogovtsev; Ia. A. Korenovska; E. V. Glinyanaya. On some random integral operators generated by an Arratia flow. Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 8-18. http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a1/