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Title: Regularly varying random fields and local sequence alignment Authors:  Hrvoje Planinic - Faculty of Science, University of Zagreb (Croatia) [presenting]
Bojan Basrak - Faculty of Science, University of Zagreb (Croatia)
Abstract: When considering ungapped local alignments of two independent i.i.d. sequences of letters from a finite alphabet, one usually constructs a (random) matrix which summarizes the local alignment scores. Under mild conditions, extreme values of this matrix appear in clusters along the diagonals, and it is known the number of such clusters is asymptotically Poisson distributed. This problem is motivated by applications in comparision of biological sequences. We discuss that, under suitable transformations, this problem can be analyzed using the theory of stationary regularly varying random fields, the key tool being the so--called tail process. In particular, using point processes we show that all extremes of the score matrix can asymptotically be approximated by a certain Poisson cluster process which is fully determined by the tail process.