Random walk

From the last few days, I have been spending my time reading about randomness and chaos and want to share something very basic yet insightful - Random Walk.

Ever wondered that when you go for morning / evening walk, many times you end up meeting the same people from your neighborhood and sometimes you meet them at the same time in every walk, even though your walk time and the path is random. So is random walk really random?

What is Random Walk?

A random walk is a process of taking successive steps in a randomized fashion. Imagine you are about to go for a morning walk. Suppose at every step you take a decision of the direction you want to take the next step at and there is a probability assigned to each direction that you will move in. The complete walk after several steps is called the random walk.

Types of Random Walk?

Random walks can also take place on a variety of spaces: commonly studied ones include graphs, integers or the real line. It is also studied on higher-dimensional vector spaces, curved surfaces or groups.

Some random walks appear to be path-dependent and cover same path while others seem to ignore their past behaviour and end up converging with other paths with different histories.

What this means is that some walks can turn out to be predicable one while others can be not as predictable as others and may look stochastic. Many times the change in initial condition for the walk can change the future course of action. Brownian motion is a specific type of random walk.

Applications?

Biologists can use random walks to model how animals move while physicists use it to model how particles behave. In financial economics, it is experimented to be used to model shares prices.

Genetic drift is studied by population genetics as a case for a random walk. Other applications include epidemiology, polymer science, image processing and segmentation, psychology, behavioral economics, gambling, recommendation system among others.

Random walks have also been used in massive online graphs such as online social networks and making recommendations over the graph

So is the random walk really random?

Is random walk truly random or it does it have some form of memory? A recent paper tries to answer some of these questions https://authors.library.caltech.edu/97403/ . As the author explains:

Say you have two societies, and one of them makes some technological advancement while the other suffers a natural disaster. Are these differences going to persist forever, or will they eventually disappear and we'll forget that once there was an advantage? In random walks, it has been long known that there are groups that have these memories while in other groups the memories are erased. But it was not really clear which groups have this property and which don't—that is, what makes a group have memory? — Omer Tamuz

read more: https://www.caltech.edu/about/news/math-professor-and-students-take-random-walk-together

Corona Modelling and Random Walk?

While studying random walk, I came across the following paper:

Akay, Haluk, and George Barbastathis. "MARKOVIAN RANDOM WALK MODELING AND VISUALIZATION OF THE EPIDEMIC SPREAD OF COVID-19." medRxiv (2020).APA

Link: https://www.medrxiv.org/content/10.1101/2020.04.12.20062927v1.full.pdf

Abstract: The epidemic spread of CoVID-19 has resulted in confirmed cases of viral respiratory illness in more than 1.4 million people around the world as of April 7th, 2020. However, different regions have experienced the spread of this disease differently. Here, we develop a Markovian random-walk spatial extension of a quarantine-enhanced SIR model to measure, visualize and forecast the effect of susceptible population density, testing rate, and social distancing and quarantine policies on epidemic spreading. The model is used to simulate the spread of CoVID-19 in the regions of Hubei, China; South Korea; Iran; and Spain. The model allows for evaluating the results of different policies both quantitatively and visually as a means of better understanding and controlling the spread of the disease

Code

Those who want to begin coding on RW can start from here.

Presentation

..coming up soon.

Community

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The idea behind the series is to share a community reading list and explore new ideas. This newsletter is a spin-off of an everyday AI session series where we pick one topic of AI a day and discussed that.

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