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The low-temperature specific heat (SH) of overdoped La 2−x Sr x CuO 4 single crystals (0.178 x 0.290) has been measured. For the superconducting samples (0.178x 0.238), the derived gap values (without any adjusting parameters) approach closely onto the theoretical prediction ∆ 0 = 2.14k B T c for the weak-coupling d-wave BCS superconductivity. In addition, the residual term γ(0) of SH at H = 0 increases with x dramatically when beyond x ∼ 0.22, and finally evolves into the value of a complete normal metallic state at higher doping levels, indicating growing amount of unpaired electrons. We argue that this large γ(0) cannot be simply attributed to the pair breaking induced by the impurity scattering, instead the phase separation is possible. PACS numbers: 74.25.Bt,74.20.Rp, 74.25.Dw, 74.72.Dn c = 1 − 82.6(x − 0.16) 2 with T max c = 38 K. The SH measurements were performed on an Oxford Maglab cryogenic system using the thermal relaxation technique, as described in detail previously. 19 The temperature was down to 1.9 K and the magnetic field was applied parallel to c-axis in the measurements.

We give a general approach to infinite dimensional non-Gaussian Analysis which generalizes the work [ADKS94] to measures which possess more singular logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.