Probability Theory

Salvatore Torquato gives a public lecture in the Simons Foundation's 2026 Randomness series, connecting the geometry of complex systems with random structures and applications across mathematics, computer science, physics and chemistry.

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamical version of the optimal transport problem. Indeed, the Schrodinger bridge looks for the most probable path in probability distribution space, which connects two given probabilities. The Schrodinger bridge problem, originally devised for freely diffusing particles, can be generalized to the case of interacting particles. It can be formulated in terms of functional integrals over bosonic fields, which allows us to derive partial differential equations that characterize the most probable paths in probability space. CARL VAN VREESWIJK MEMORIAL LECTURE 2026. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-04-15. Recording duration: 00:55:05.

Develop and apply quantum resource theory for Extended Wigner’s Friend scenarios, where the presence of another observer can affect measurement outcomes. The work involves analytical quantum information and probability theory, together with numerical simulation, and relates to Bell nonlocality. This FAPESP-funded doctoral position is expected to start in March 2027. Apply by 16 November 2026 with a CV, a motivation letter of up to two pages and contact information for two academic referees, following the official advertisement.

Develop and apply quantum resource theory for Extended Wigner’s Friend scenarios, where the presence of another observer can affect measurement outcomes. The work involves analytical quantum information and probability theory, together with numerical simulation, and relates to Bell nonlocality. This FAPESP-funded doctoral position is expected to start in March 2027. Apply by 16 November 2026 with a CV, a motivation letter of up to two pages and contact information for two academic referees, following the official advertisement.

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamical version of the optimal transport problem. Indeed, the Schrodinger bridge looks for the most probable path in probability distribution space, which connects two given probabilities. The Schrodinger bridge problem, originally devised for freely diffusing particles, can be generalized to the case of interacting particles. It can be formulated in terms of functional integrals over bosonic fields, which allows us to derive partial differential equations that characterize the most probable paths in probability space. CARL VAN VREESWIJK MEMORIAL LECTURE 2026. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-04-15. Recording duration: 00:55:05.