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Santosh S. Venkatesh

Department of Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, PA

Professor of Electrical and Systems Engineering

Former Chair of the Faculty Senate

From left: 1. Paris, circa 1576 [Notes on Fourier Analysis]; 2. Viète’s formula — [The Theory of Probability]; 3. coins from antiquity — [Video Lectures on Probability]

Paris, circa 1576:

The isoperimetric priniciple in action

Viète’s formula:

The link between number theory & probability


Coins from antiquity:

The ancient science of chance

TEDx Penn 2022

Probability weaves an intricate thread through life, never more tragically visible than in times of catastrophe like wars, hurricanes, financial collapses, and pandemics.  An accidental discovery in the mathematical theory of chance dating to the immediate aftermath of the French Revolution remarkably provides a skein connecting all these apparently disparate, chance-driven events, and provides a startling clarity of vision. In this talk I explore the ramifications of this discovery in realms apparently far apart, starting from the sad story of a birthday cake and proceeding to a once-in-a-century pandemic which has changed the lives of all the world's inhabitants — with a detour through mishaps in trials by jury and a side-helping of war and devastation — and discover an elegant commonality and simplicity of understanding of the progress of these complex events. This talk was given at a TEDx event using the TED conference format.

Clarity amid catastrophe—understanding chance | Santosh Venkatesh | TEDxPenn
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A rich and sumptuous book, a quarter-century in the making, which tackles the foundations of the mathematical theory of probability in a vibrant historical tapestry, made lush by riotous application, ancient and modern.

On-line video lectures

The video snippet below is the introductory video lecture in a suite of videos which invites the curious viewer into the magical world of probability. These video lectures originally appeared as a top-rated MOOC on Coursera in 2015.  In total these lectures cover material equivalent to a semester course on undergraduate probability at the University of Pennsylvania where this academic has taught since 1986.  Follow the link to the Video Lectures page for the full collection of video lectures.


This is a long page and, depending on the viewer's internet speed, may take a browser a short while to load the video thumbnails. Video playback should be delay-free from that point on.

The Courses page contains ancillary information to go with the video lectures: in the Probability folder viewers will find a summary of what they can expect to see as they wind their way through the suite of video lectures and what they can hope to learn, supporting documents, problem sets, and solutions.

Probability: the mathematical theory of chance — [Probability | Santosh S. Venkatesh]
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& Articles

I grew so rich that I was sent

By a pocket borough into Parliament.

I always voted at my party's call

And I never thought of thinking for myself at all.

— W. S. Gilbert, H. M. S. Pinafore

Over a long career, my research interests have been piqued by questions in pure and applied probability, applied mathematics, information theory, machine learning, neural networks, computation and complexity theory, epidemic modelling, and mathematical economics.  Current research questions that have a hold on my attention include:

  • In probability theory: the phenomenon of concentration of measure in random matrices with weak dependency structures.

  • In mathematical economics: what conditions in a diversified financial network can lead to contagion and systemic failure?

  • In social network theory: what explains the spread of polarisation in social and political networks?

  • In combinatorics: variations on a classical theme of Littlewood and Offord.

For articles on current and earlier work, read on.

From left: 1. How to cross a deep river per Francis Galton, and the origins of statistical regression — [The Theory of Probability]; 2. Erdös–Rényi graphs, physical distancing, and pandemics — [Epidemic Modelling]; 3. Dido of Tyre and Gaussian isoperimetry — [The Theory of Probability]; 4. Mosaic processes and connectivity in geometric random graphs — [Random Graph Theory]

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