WEBVTT 00:00:01.352 --> 00:00:03.732 The random walk model provides a simple way 00:00:03.732 --> 00:00:06.112 to represent to complex random movements 00:00:06.112 --> 00:00:08.370 of many everyday objects such as 00:00:08.370 --> 00:00:11.170 the wiggly motion of air molecules in a room, 00:00:11.170 --> 00:00:14.140 the dispersion of a drop of food coloring in water. 00:00:14.140 --> 00:00:17.850 or the ups and downs of stock prices over time. 00:00:17.850 --> 00:00:20.188 To be concrete, suppose you could sit on 00:00:20.188 --> 00:00:22.790 an oxygen molecule in the air and you could 00:00:22.790 --> 00:00:26.130 actually see the world at the molecular scale. 00:00:26.130 --> 00:00:27.790 What would you see? 00:00:27.790 --> 00:00:31.050 You’d be zooming at roughly three hundred meters at a second. 00:00:31.050 --> 00:00:33.050 However before moving very far, 00:00:33.050 --> 00:00:37.770 you bashed into another air molecule at roughly the same speed. 00:00:37.770 --> 00:00:41.310 Each such collision happens roughly everyone by into a second. 00:00:41.310 --> 00:00:44.260 So your trajectory would consist of very short periods 00:00:44.260 --> 00:00:47.010 of free motion interrupted by collision 00:00:47.010 --> 00:00:49.930 to drastically change your direction. 00:00:49.930 --> 00:00:51.350 Think of bumper cars 00:00:51.350 --> 00:00:53.310 but speed up by factor of a hundred 00:00:53.310 --> 00:00:56.310 and shrunk by factor of ten billion. 00:00:56.310 --> 00:00:57.960 The motion of your oxygen molecule 00:00:57.960 --> 00:01:01.890 will be dominated by all these collisions. 00:01:01.890 --> 00:01:04.920 The motion of all microscopic particles, 00:01:04.920 --> 00:01:07.480 for example, molecules, cells and 00:01:07.480 --> 00:01:10.450 pollens can be described in this way. 00:01:10.450 --> 00:01:12.460 However keeping track of all these 00:01:12.460 --> 00:01:15.080 collisions between microscopic particles 00:01:15.080 --> 00:01:18.280 and all the other particles in environment 00:01:18.280 --> 00:01:20.680 is hopelessly complicated. 00:01:20.680 --> 00:01:24.500 So instead we use a simplifying mathematical model 00:01:24.500 --> 00:01:27.980 to account for this complex phenomenon 00:01:27.980 --> 00:01:30.840 in the case of an air molecule, it is much simpler 00:01:30.840 --> 00:01:34.290 to represent its movement as a random walk. 00:01:34.290 --> 00:01:37.080 In the random walk model, we nearly say 00:01:37.080 --> 00:01:39.300 that a particle changes its direction 00:01:39.300 --> 00:01:42.760 and its speed at random times. 00:01:42.760 --> 00:01:45.110 These changes and perspectives from collision 00:01:45.110 --> 00:01:47.240 between many particles to a single 00:01:47.240 --> 00:01:50.710 randomly moving particle is enormously simplified. 00:01:50.710 --> 00:01:53.150 You can use the random walk model to ask 00:01:53.150 --> 00:01:55.710 and answer many important questions, 00:01:55.710 --> 00:02:01.010 like, how far does a particle travel in a given amount of time? 00:02:01.010 --> 00:02:05.670 What is the distribution of distances the particle travels? 00:02:05.670 --> 00:02:09.660 Or how long does it take for a particle to move a given distance? 00:02:09.660 --> 00:02:12.170 In addition to understanding the motion of a particle 00:02:12.170 --> 00:02:15.180 in a microscopic world, the random walk model 00:02:15.180 --> 00:02:20.170 has many other important applications of larger scales. 00:02:20.170 --> 00:02:25.330 How much would you expect to win or lose over time to gambling? 00:02:25.330 --> 00:02:29.090 How does a stock market fluctuate up and down? 00:02:29.090 --> 00:02:31.676 When do random fluctuations in voltage cause 00:02:31.676 --> 00:02:34.586 a neuron in your brain to fire? 00:02:34.586 --> 00:02:36.886 Or how do cultural ideas get pass from 00:02:36.886 --> 00:02:39.276 one person to another in societies? 00:02:39.276 --> 00:02:41.316 Applying the mathematics of random walk’s 00:02:41.316 --> 00:02:45.086 to these kinds of questions, represents some of the research 00:02:45.086 --> 00:02:48.216 that we do here at the Santa Fe Institute.