ABSTRACT
The terminology of urns and urn models generally refers to a system of one or more urns containing objects of various types. One customarily calls the objects balls and distinguishes the object types by colors. Thus, in the usual setting there are colored balls in one or more urns. The system then evolves in time, subject to rules of throwing balls into the urns or drawing balls under predesignated replacement schemes. The rule, for example, might be to draw a ball at random (all balls being equally likely) and put it back in the urn together with another ball of the same color. The equally likely assumption in drawing a ball is usually thought of as an effect of purposeful randomization. It can be approximated reasonably well by shaking the urn well before a draw to induce good mixing of its contents.
