From 9b33046355238f56cda18493b8c757db736516a4 Mon Sep 17 00:00:00 2001
From: Urbain Vaes <urbain@vaes.uk>
Date: Thu, 21 Sep 2023 18:37:50 +0200
Subject: Add worked example

---
 figures.jl | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)
 create mode 100644 figures.jl

(limited to 'figures.jl')

diff --git a/figures.jl b/figures.jl
new file mode 100644
index 0000000..ed9b70f
--- /dev/null
+++ b/figures.jl
@@ -0,0 +1,17 @@
+using Plots
+using QuadGK
+using LaTeXStrings
+
+V(x) = 1 - cos(x)
+η = .1
+
+# plot(title="Invariant distribution of perturbed OL") 
+plot(title="") 
+for η ∈ [0, .5, 1, 2]
+    ρ(q) = exp(-V(q)) * quadgk(y -> exp(V(q + y) - η*y), 0, 2π)[1]
+    Z = quadgk(ρ, - π, π)[1]
+    plot!(q -> ρ(q) / Z, -π, π, label=L"\eta = " * string(η), lw=2)
+end
+plot!(xlims = (-π, π), grid=false, ylims=(0, .4), framestyle=:box)
+savefig("figures/invariant_perturbed_ol.pdf")
+
-- 
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