Fig. 4

Finite asymptotic limit of covariances$a_{ij}$and correlation coefficient${\rho }_T$. a Count covariance $a_{12}={\sum }_{q=1}^{\mathrm{\infty }}{\sigma }_{X_1,X_2}^2(q)$ vs. time bin T for varying correlation strengths r in the case of two identical neurons. The covariances converge for increasing time bin T towards the value predicted in Theorem 4.1 (indicated by small, thick lines). Here ${\tau }_s=1$, and $\psi =0.3$. b Limit value of the covariance $a_{12}$ vs. r for $T=20{\tau }_s$ (from a) vs. r. The case of $r=1$ (black) corresponds to the variance $a_{11}\approx 5.5\cdot {10}^{-3}$, indicated by the dashed horizontal line. c Correlation coefficient ${\rho }_T$ vs. r for large time bins ($T=20{\tau }_s$). The dashed line indicates the equality line