An anticyclone is a weather system that is characterized by high pressure. Therefore, statement 1 is correct. In an anticyclone, the air in the center of the system is subsiding, which means it is sinking towards the surface. This is because as the air sinks, it warms up and leads to the development of higher pressure. Therefore, statement 2 is correct.

However, anticyclones are not characterized by converging winds. In fact, they are characterized by diverging winds. As the air sinks in the center of the anticyclone, it spreads outwards in a clockwise direction in the Northern Hemisphere and in an anti-clockwise direction in the Southern Hemisphere. This results in the divergence of winds away from the center of the anticyclone. Therefore, statement 3 is incorrect.

Therefore, out of the given statements, only statements 1 and 2 are correct. The correct answer is 2.