# Spontaneous clustering in theoretical and some empirical stationary processes*

T. Downarowicz; Y. Lacroix; D. Léandri

ESAIM: Probability and Statistics (2010)

- Volume: 14, page 256-262
- ISSN: 1292-8100

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topDownarowicz, T., Lacroix, Y., and Léandri, D.. "Spontaneous clustering in theoretical and some empirical stationary processes*." ESAIM: Probability and Statistics 14 (2010): 256-262. <http://eudml.org/doc/250850>.

@article{Downarowicz2010,

abstract = {
In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased
frequency separated by longer breaks. Such behavior, contradicting the theoretical “unbiased behavior” with exponential
distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to explain.
In the last section we relate one such empirical example of clustering, in the area of marine technology. In the theoretical part of the
paper we prove, using ergodic theory and the notion of category, that clustering (even very strong) is in fact typical for
“rare events” defined as long cylinder sets in processes generated by a finite partition of an arbitrary (infinite aperiodic)
ergodic measure preserving transformation.
},

author = {Downarowicz, T., Lacroix, Y., Léandri, D.},

journal = {ESAIM: Probability and Statistics},

keywords = {Stationary random process; return time; hitting time; attracting; limit law; cluster; the law of series; stationary random process},

language = {eng},

month = {10},

pages = {256-262},

publisher = {EDP Sciences},

title = {Spontaneous clustering in theoretical and some empirical stationary processes*},

url = {http://eudml.org/doc/250850},

volume = {14},

year = {2010},

}

TY - JOUR

AU - Downarowicz, T.

AU - Lacroix, Y.

AU - Léandri, D.

TI - Spontaneous clustering in theoretical and some empirical stationary processes*

JO - ESAIM: Probability and Statistics

DA - 2010/10//

PB - EDP Sciences

VL - 14

SP - 256

EP - 262

AB -
In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased
frequency separated by longer breaks. Such behavior, contradicting the theoretical “unbiased behavior” with exponential
distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to explain.
In the last section we relate one such empirical example of clustering, in the area of marine technology. In the theoretical part of the
paper we prove, using ergodic theory and the notion of category, that clustering (even very strong) is in fact typical for
“rare events” defined as long cylinder sets in processes generated by a finite partition of an arbitrary (infinite aperiodic)
ergodic measure preserving transformation.

LA - eng

KW - Stationary random process; return time; hitting time; attracting; limit law; cluster; the law of series; stationary random process

UR - http://eudml.org/doc/250850

ER -

## References

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