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Almost Sure

@Almost_Sure • 8,918 subscribers

George Lowther, Author of Almost Sure blog, on maths, probability and stochastic calculus. Also on YouTube https://t.co/VyOijwbe9l

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Quick "proof" of Taylor expansion using operator exponential

Quick "proof" of Taylor expansion using operator exponential

25,027 次观看

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"everything is linear if you zoom in close enough..."

"everything is linear if you zoom in close enough..."

1,019,199 次观看 • 6 个月前

Animating the solution to this surprisingly interesting fruity math problem:

Animating the solution to this surprisingly interesting fruity math problem:

87,534 次观看 • 1 个月前

in quantum physics position X and momentum P can’t be simultaneously measured. But, linear combinations aX+bP 𝘢𝘳𝘦 observable, and their distributions can be used to back out the joint X,P probability density. The Wigner distribution but, it is 𝘸𝘦𝘪𝘳𝘥

in quantum physics position X and momentum P can’t be simultaneously measured. But, linear combinations aX+bP 𝘢𝘳𝘦 observable, and their distributions can be used to back out the joint X,P probability density. The Wigner distribution but, it is 𝘸𝘦𝘪𝘳𝘥

70,143 次观看 • 3 个月前

What software do math YouTubers use to do the fancy math animations?

What software do math YouTubers use to do the fancy math animations?

274,162 次观看 • 2 年前

stylistic question. In YouTube, color coding terms in math formulas. Yes, or no?

stylistic question. In YouTube, color coding terms in math formulas. Yes, or no?

43,677 次观看 • 3 个月前

Let X = exp(A²/2) and Y=exp(B²/2) where A,B are joint normal with mean 0, variance 1, and correlation ρ (between 0 and 1). Then, E[X|Y] = Y/ρ > Y E[Y|X] = X/ρ > X So X is greater than Y 'on average', and Y is greater than X on average. Here's a proof of that

Let X = exp(A²/2) and Y=exp(B²/2) where A,B are joint normal with mean 0, variance 1, and correlation ρ (between 0 and 1). Then, E[X|Y] = Y/ρ > Y E[Y|X] = X/ρ > X So X is greater than Y 'on average', and Y is greater than X on average. Here's a proof of that

31,334 次观看 • 8 个月前

Here's a smooth plot of zᶻ as z rotates 4 times round the unit circle at unit speed

Here's a smooth plot of zᶻ as z rotates 4 times round the unit circle at unit speed

26,283 次观看 • 1 年前

A paradox of conditional expectations applied to the Ornstein-Uhlenbeck process

A paradox of conditional expectations applied to the Ornstein-Uhlenbeck process

14,994 次观看 • 8 个月前

From the Riemann zeta function to Xi and the functional equation

From the Riemann zeta function to Xi and the functional equation

13,025 次观看 • 7 个月前

Constructing Weierstrass' function. Continuous, nowhere differentiable, unbounded variation, no intervals of increase or decrease. Fractal dimension 3/2. All things it has in common with mathematical Brownian motion

Constructing Weierstrass' function. Continuous, nowhere differentiable, unbounded variation, no intervals of increase or decrease. Fractal dimension 3/2. All things it has in common with mathematical Brownian motion

11,759 次观看 • 1 年前

2025 as a sum of cubes: Nicomachus's theorem, an animated proof

2025 as a sum of cubes: Nicomachus's theorem, an animated proof

12,908 次观看 • 1 年前

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