Here are some applications of free probability of random matrices:

• Neural networks: The asymptotic freeness assumption plays a fundamental role in the study of the propagation of spectral distributions through the layers of a deep neural network, see Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron (2021) and Free Probability for predicting the performance of feed-forward fully connected neural networks (2022).
• Wireless communication: The asymptotic capacity limit of a multi-antenna channel can be calculated from the an asymptotic free probability assumptions, see Free Probability based Capacity Calculation of Multiantenna Gaussian Fading Channels with Cochannel Interference (2010).
• Quantum information: Free probability is helpful to understand the problem of the quantificatio of the degree of entanglement of a multi-qubit system, see Applications of free probability to quantum information theory (2014).

Here are some applications of free probability of random matrices:

• Neural networks: The asymptotic freeness assumption plays a fundamental role in the study of the propagation of spectral distributions through the layers of a deep neural network, see Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron (2021) and Free Probability for predicting the performance of feed-forward fully connected neural networks (2022).
• Wireless communication: The asymptotic capacity limit of a multi-antenna channel can be calculated from the an asymptotic free probability assumptions, see Free Probability based Capacity Calculation of Multiantenna Gaussian Fading Channels with Cochannel Interference (2010).
• Quantum information: Free probability is helpful to understand the problem of the quantificatio of the degree of entanglement of a multi-qubit system, see Applications of free probability to quantum information theory (2014).
• Statistical physics: The free energy of exclusion processes can be calculated using tools from free probability, see Bernoulli variables, classical exclusion processes and free probability (2022).

Asymptotic freeness assumption plays a fundamental role in the study of the propagation of spectral distributions through the layers of a deep neural network, see Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron (2021).

Here are some applications of free probability of random matrices:

• Neural networks: The asymptotic freeness assumption plays a fundamental role in the study of the propagation of spectral distributions through the layers of a deep neural network, see Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron (2021) and Free Probability for predicting the performance of feed-forward fully connected neural networks (2022).
• Wireless communication: The asymptotic capacity limit of a multi-antenna channel can be calculated from the an asymptotic free probability assumptions, see Free Probability based Capacity Calculation of Multiantenna Gaussian Fading Channels with Cochannel Interference (2010).
• Quantum information: Free probability is helpful to understand the problem of the quantificatio of the degree of entanglement of a multi-qubit system, see Applications of free probability to quantum information theory (2014).