Light variations in the shadows is called "noise."
Noise in images is a given, no matter which camera you buy, because light variations are a fact of life that all cameras have to deal with. It doesn't matter whether you shoot with a compact or an D800, the amount of noise in the shadows is a matter of physics, and the way to reduce the noise is to collect lots of light in the shadow area. You can do this two ways: by having big photo-sites (When you double the dimensions of the photo-site, the noise becomes half as objectionable.) and by leaving the shutter open four times as long (the noise is half as objectionable ) To expose to the right of the histogram (ETTR) you need a sensor with a large dynamic range to prevent the highlights from burning out due to the four times overexposure of the shadows.
Photodiodes (photo sites) are getting smaller - from 8 microns down to 1.1. microns
The problem is that photo-sites are getting smaller and smaller due to the demand for high pixel count. The MM answer was to make the sensor itself bigger (FF,) but each photo-site is small, so there is still noise in the shadows, even at moderate ISO - but it is monochromatic noise and looks like film grain, and so it is okay.
The camera with the biggest photo-sites is the Nikon D70. At its maximum ISO 1600 it can be set up to produce almost noiseless pictures - without noise reduction. What little noise is present can be fixed with a 2% NR in Nikon NX2. And the pictures are sharp and detailed.
Noise in the shadows is masked by the software in the camera.
When you see pictures posted on the WEB that claim noise free high ISO performance, you are often looking at pictures that have a lot of NR applied to them. The colors are poor, the edges blurred, the dynamic range squished down, and the blacks made solid black to hide the noise.
Noise reduction through multiple exposures
SONY has a method of reducing noise without too much blurring. The camera can be set to make six exposures rapidly and the computer combines the light from all of them, and the variations in light are swamped out (noise). I posted one made at ISO 6400 today (bookcase picture.) For more info on this capability go to
Noise reduction by combining the light from four photodiodes
FUJI lets you combine the light from four photo-sites by choosing a low resolution 1/4 of max (3MP.) For the WEB this is a reasonable way to shoot pictures as even 3MP is big for many monitors.
Camera temperature is a big noise contributor. The battery and the sensor get hot with use, and it is pretty easy to exceed the recommended temperature with ordinary use. You can get good night shots outside in the cold winter because the sensor keeps cool (astronomers cool their camera sensors with cryogenic cooling systems) - so expect to see wintertime shots in commercials. You won't get good night time high ISO shots in the tropics with small cameras. When I shoot high ISO with a compact camera, it stays in an insulated lunch box at 60 degrees until it is time to shoot, then I hold it by a small tripod screwed into the camera so my hand doesn't heat the body (which is all metal.) That way I can shoot ISO 3200, and at least avoid the purple color noise caused by the sensor temperature reaching its design limit.
The bigger the camera body, the easier it is to keep the sensor cool, because you can locate the battery (which gets hot) away from the sensor and use the housing to dissipate the heat.
The designers of small cameras use the computer power to hide these noises from the user, by blurring and smearing the colors. But the image isn't pretty.
If you shoot in B&W, the noise is much less objectionable, because it is monochromatic.
Front side illuminated sensors FSI (most cameras have this type RX 100, NEX-3 - 7) versus Back Side Illuminated sensors (BSI.)
SONYS newest cameras are using BSI sensors (RX100 II, RX 10) and this increases the light at the sensor by 1 dB (about 25%) but the fact that the lenses used to focus the light on the diode, are very wide angle, causes problems. In the end the performance of the FSI and BSI sensors for these cameras, are about the same. As photo sites become smaller (1.1 micron is the new goal,) driven by the never ending pursuit of cost reduction, BSI advantages will outweigh FSI designs. None of the CMOS sensors are as good at collecting light as CCD, used on older camera designs, but they are cheaper, and you can use them to make HD movies, which is an advantage to surveillance cameras for which there is a huge and growing market.