Lagrangian space consistency relation for large scale structure

Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present. The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.Comment: 19 pages, no figure

Intraday pattern in bid-ask spreads and its power-law relaxation for Chinese A-share stocks

We use high-frequency data of 1364 Chinese A-share stocks traded on the Shanghai Stock Exchange and Shenzhen Stock Exchange to investigate the intraday patterns in the bid-ask spreads. The daily periodicity in the spread time series is confirmed by Lomb analysis and the intraday bid-ask spreads are found to exhibit $L$-shaped pattern with idiosyncratic fine structure. The intraday spread of individual stocks relaxes as a power law within the first hour of the continuous double auction from 9:30AM to 10:30AM with exponents $\beta_{\rm{SHSE}}=0.19\pm0.069$ for the Shanghai market and $\beta_{\rm{SZSE}}=0.18\pm0.067$ for the Shenzhen market. The power-law relaxation exponent $\beta$ of individual stocks is roughly normally distributed. There is evidence showing that the accumulation of information widening the spread is an endogenous process.Comment: 12 Elsart pages including 7 eps figure