arXiv subjects

Christian Mazza

Publications and source records attributed to Christian Mazza.

21 records · Page 2Linked to original sources

arXiv2004

Long time behavior of the solutions to non-linear Kraichnan equations

We consider the solution of a nonlinear Kraichnan equation $$\partial_s H(s,t)=\int_t^s H(s,u)H(u,t) k(s,u) du,\quad s\ge t$$ with a covariance kernel $k$ and boundary condition $H(t,t)=1$. We study the long time behaviour of $H$ as the time parameters $t,s$ go to infinity, according to the asymptotic behaviour of $k$. This question appears in various subjects since it is related with the analysis of the asymptotic behaviour of the trace of non-commutative processes satisfying a linear differential equation, but also naturally shows up in the study of the so-called response function and aging properties of the dynamics of some disordered spin systems.

math.PR↗

arXiv2004

Simply Generated Trees, B-series and Wigner Processes

We consider simply generated trees and study multiplicative functions on rooted plane trees. We show that the associated generating functions satisfy differential equations or difference equations. Our approach considers B-series from Butcher's theory, the generating functions are seen as generalized Runge-Kutta methods

math.CO↗

arXiv2003

Strand separation in negatively supercoiled dna

We consider a model for strand separation in negatively supercoiled dna, and study the effect of supercoiling on the localization of denaturation, using notions from statistical mechanics. The model is based on on mean field Ising system, coupled with a random field one dimensional ISing model. The effect of the word in AT and Gc associated with the DNA on localization of denaturation is studied under the hypothesis of small perimeter.

cond-mat.stat-mech↗