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6 results
Clear filtersHeat.gaussian_tail_bound_by_weighted
Plain-language statement
Key Gaussian tail bound: This is the analytical estimate that allows us to bound Gaussian tail integrals and prove convergence as t → 0.
Source project: PDE
Person-level attribution pending.
Heat.heatKernel_mass_one_x_sub_y_even
Plain-language statement
Translation Invariance: The heat kernel integrates to 1 regardless of translation. -
Source project: PDE
Person-level attribution pending.
Heat.heatTail_changeOfVariables
Plain-language statement
Change of variables formula for heat kernel tail integrals. Transforms the integral ∫_{|y-x| ≥ δ} Φ(x-y,t) dy into a standard Gaussian tail integral via the substitution z = (x-y)/√(4αt).
Source project: PDE
Person-level attribution pending.
Heat.integral_indicator_tail_even
Plain-language statement
For even functions, the two-sided tail integral equals twice the one-sided integral.
Source project: PDE
Person-level attribution pending.
Heat.integral_mul_exp_neg_sq_Ici_zero
Plain-language statement
Evaluation of ∫₀^∞ z exp(-z²) dz = 1/2.
Source project: PDE
Person-level attribution pending.
Heat.integral_split_near_far
Project documentation
Helper lemma for splitting integrals into near and far regions.
Source project: PDE
Person-level attribution pending.