On the segment the energy contains
$$
c_3\int_0^1\int_0^1\frac{ds\,dt}{|s-t|},
$$
which diverges logarithmically along the diagonal. The uniform segment measure therefore has infinite Green energy, so its mean cannot be defined as an $L^2$ Gaussian-field pairing.


Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 209 / 5 / A2 / Segment / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-209/5/a2/segment/solution