EndpointLimit.lean`

1 declarations, 0 contain sorry, 0 declared as axioms

theorem OAI.GammaFPP.CrossingBridge.gamma_arbitraryEndpoint_tendsto_of_grids line 15

Source documentation

The arbitrary-endpoint probability tends to zero when the grid-failure tail tends to zero.

theorem gamma_arbitraryEndpoint_tendsto_of_grids {ι : Type*} {l : Filter ι}
    (henv : GammaEnvironment shape rate P τ)
    (hshape : 0 < shape) (hrate : 0 < rate)
    (b K A R ε q₀ : ℝ) (hb : |b| ≤ 1) (hK : 100 ≤ K)
    (hA : 0 < A) (hR : 0 < R) (hε : 0 < ε) (hq : 0 < q₀) (plus : Bool)
    (k m : ι → ℕ) (hk : Tendsto k l atTop)
    (hratio : Tendsto (fun i => (2 : ℝ)^(m i)/(2 : ℝ)^(k i)) l atTop)
    (hm : ∀ᶠ i in l, m i ≤ 3*k i)
    (hgrid : ∀ J : ℕ, 1 ≤ J → ∀ᶠ i in l,
      P.real {ω | (fun e => τ e ω) ∉ gridConnectionsEvent shape rate b ((gammaMeanNorm henv hshape hrate) (direction b)) K A R (k i) (m i) J} ≤
        Grid.gridFailureTail shape (gridIndexConstant A R) q₀ J) :
    Tendsto (fun i => P.real {ω | (fun e => τ e ω) ∈ arbitraryEndpointEvent b ((gammaMeanNorm henv hshape hrate) (direction b))
…

Mentions: OAI.GammaFPP.GammaEnvironment, OAI.GammaFPP.CrossingBridge.gridConnectionsEvent, OAI.GammaFPP.gammaMeanNorm, OAI.GammaFPP.Grid.gridFailureTail, OAI.GammaFPP.CrossingBridge.gridIndexConstant, OAI.GammaFPP.CrossingBridge.arbitraryEndpointEvent