![]() By proving that a statistical mechanics description could explain quantitatively brownian motion, all doubts concerning Boltzmann's statistical interpretation of the thermodynamic laws suddenly faded. We would therefore like to be able to describe a motion similar to the random walk above, but where the molecule can move in all directions. ![]() As Einstein himself remarked, the consequence of this relation is that one can see, directly through a microscope, a fraction of the thermal energy manifest as mechanical energy. Brownian motion Real gas molecules can move in all directions, not just to neighbors on a chessboard. This finding went beyond simply confirming the existence of atoms and molecules, and provided a new way of determining Avogadro's number. This connection between displacement, x( t), and the viscosity, η, can be expressed (in one dimension) as: 〈x(t) 2 〉 = RT t/(3 Nπaη), where R is the universal gas constant, N is Avogadro's number (2 R/3 N is Boltzmann's constant k B), T is the temperature and a is the radius of the suspended particles. In particular, Einstein showed that the irregular motion of the suspended particles could be understood as arising from the random thermal agitation of the molecules in the surrounding liquid: these smaller entities act both as the driving force for the brownian fluctuations (through the impact of the liquid molecules on the larger particles), and as a means of damping these motions (through the viscosity experienced by the larger particles). Brownian Motion is caused by collisions between microscopic particles such as atoms and molecules within any fluid and the particles of interest. Brownian motion is an example of a random walk model because the trait value changes randomly, in both direction and distance, over any time interval. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. ![]() It was in this context that Einstein's explanation for brownian motion made an initial impression. The Brownian motion models for financial markets are based on the work of Robert C. ![]()
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