What causes the small peak at the start of the spectrum in a spectrum analyzer?
Many conjectures may be conceived on this evident phenomenon.

One might think it is due by leaking of low-frequency components that are out-of-band and feature a large amplitude. However, selectivity and attenuation of the IF filter are enough to filter out such components.
In reality it is caused by leakage of the Local Oscillator into the IF signal path: if you measure a low frequency, this is converted by the mixer to a signal whose frequency is close the the LO one, from which the false reading of higher-than-expected amplitude. [taken from my book &quot;RF and Microwave Measurements&quot;, sec. 9.2.6]

From a wider perspective there are other phenomena that might look similar:

flicker noise, with 1/f profile;
snow-drift profile of the FFT/DFT numeric noise.