Bidenbaka
@bidenbaka.bsky.social
Math PhD | Probabilist | Illenium | Madridista
Brownian motion, Markov process
Brownian motion, Markov process
There are beautiful math, there are ugly math, and there are ugly math, whose elengance can only be appreciated after suffering.
May 27, 2025 at 4:15 AM
There are beautiful math, there are ugly math, and there are ugly math, whose elengance can only be appreciated after suffering.
Zahl presenting one of the most important results in analysis over the past 20 years — The Kakeya Conjecture
April 17, 2025 at 9:58 AM
Zahl presenting one of the most important results in analysis over the past 20 years — The Kakeya Conjecture
We know that the Hausdorff dimension is smaller equal to the Lower Box (LB) dimension and hence the Upper Box (UB) dimension. We also know that the Packing dimension is greater equal to the Hausdorff dimension but smaller equal to the UB dimension. Is there a criterion to tell when LB <= Packing dim
April 11, 2025 at 5:28 AM
We know that the Hausdorff dimension is smaller equal to the Lower Box (LB) dimension and hence the Upper Box (UB) dimension. We also know that the Packing dimension is greater equal to the Hausdorff dimension but smaller equal to the UB dimension. Is there a criterion to tell when LB <= Packing dim
Reposted by Bidenbaka
Ehsan Abedi: Processes on Wasserstein spaces and energy-minimizing particle representations in fractional Sobolev spaces https://arxiv.org/abs/2503.10859 https://arxiv.org/pdf/2503.10859 https://arxiv.org/html/2503.10859
March 17, 2025 at 6:05 AM
Ehsan Abedi: Processes on Wasserstein spaces and energy-minimizing particle representations in fractional Sobolev spaces https://arxiv.org/abs/2503.10859 https://arxiv.org/pdf/2503.10859 https://arxiv.org/html/2503.10859
Reposted by Bidenbaka
I am happy to announce that the Kakeya set conjecture, one of the most sought after open problems in geometric measure theory, has now been proven (in three dimensions) by Hong Wang and Joshua Zahl! arxiv.org/abs/2502.17655 I discuss some ideas of the proof at terrytao.wordpress.com/2025/02/25/t...
Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions
We study sets of $δ$ tubes in $\mathbb{R}^3$, with the property that not too many tubes can be contained inside a common convex set $V$. We show that the union of tubes from such a set must have almos...
arxiv.org
February 26, 2025 at 4:49 AM
I am happy to announce that the Kakeya set conjecture, one of the most sought after open problems in geometric measure theory, has now been proven (in three dimensions) by Hong Wang and Joshua Zahl! arxiv.org/abs/2502.17655 I discuss some ideas of the proof at terrytao.wordpress.com/2025/02/25/t...
Today I am reading Peres and Pörter's Brownian motion. In the part of deriving the Frostman's lemma, the original context states that $A\subset\mathbb{R}^d$ is a closed set while in other contexts $A$ is assumed to be compact. I reached to Deepseek and this prized goofy states this...
February 11, 2025 at 6:13 AM
Today I am reading Peres and Pörter's Brownian motion. In the part of deriving the Frostman's lemma, the original context states that $A\subset\mathbb{R}^d$ is a closed set while in other contexts $A$ is assumed to be compact. I reached to Deepseek and this prized goofy states this...
I am recently reading LeGall's Brownian motion. There is a step in proving Martingale Representation Theorem (Theorem 5.18) I don't understand (see Figure 1). The idea in proving assertion (i) is to use $\mathcal{H}$ to denote all such $Z$ in $L^2$, then prove it is a closed subspace (see Figure 2).
January 16, 2025 at 5:02 AM
I am recently reading LeGall's Brownian motion. There is a step in proving Martingale Representation Theorem (Theorem 5.18) I don't understand (see Figure 1). The idea in proving assertion (i) is to use $\mathcal{H}$ to denote all such $Z$ in $L^2$, then prove it is a closed subspace (see Figure 2).