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• W3100795780 abstract "Broadly distributed random variables with a power-law distribution $f(m) sim m^{-(1+alpha)}$ are known to generate condensation effects, in the sense that, when the exponent $alpha$ lies in a certain interval, the largest variable in a sum of $N$ (independent and identically distributed) terms is for large $N$ of the same order as the sum itself. In particular, when the distribution has infinite mean ($0<alpha<1$) one finds unconstrained condensation, whereas for $alpha>1$ constrained condensation takes places fixing the total mass to a large enough value $M=sum_{i=1}^N m_i > M_c$. In both cases, a standard indicator of the condensation phenomenon is the participation ratio $Y_k=langle sum_i m_i^k / (sum_i m_i)^krangle$ ($k>1$), which takes a finite value for $N to infty$ when condensation occurs. To better understand the connection between constrained and unconstrained condensation, we study here the situation when the total mass is fixed to a superextensive value $M sim N^{1+delta}$ ($delta >0$), hence interpolating between the unconstrained condensation case (where the typical value of the total mass scales as $Msim N^{1/alpha}$ for $alpha<1$) and the extensive constrained mass. In particular we show that for exponents $alpha<1$ a condensate phase for values $delta > delta_c=1/alpha-1$ is separated from a homogeneous phase at $delta < delta_c$ by a transition line, $delta=delta_c$, where a weak condensation phenomenon takes place. We focus on the evaluation of the participation ratio as a generic indicator of condensation, also recalling or presenting results in the standard cases of unconstrained mass and of fixed extensive mass." @default.
• W3100795780 created "2020-11-23" @default.
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• W3100795780 date "2017-09-26" @default.
• W3100795780 modified "2023-10-18" @default.
• W3100795780 title "Participation Ratio for Constraint-Driven Condensation with Superextensive Mass" @default.
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• W3100795780 doi "https://doi.org/10.3390/e19100517" @default.
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