B i m
C i m
ρ m , l ( N )
x i
Empirical distribution of individuals that follow a medium 𝑚 and influencer 𝑙 at time 𝑡 by the sum of Dirac delta distributions δ placed at the individuals’ opinions. This distribution describes the stochastic opinion instances at a given time and integrates to ∫ᴰ ρₘ,ₗ⁽ᴺ⁾(𝑥, 𝑡) 𝑑𝑥 ≔ 𝑛ₘ,ₗ⁽ᴺ⁾(𝑡), the proportion of individuals that follow medium 𝑚 and influencer 𝑙.
ρ m , l ( N ) ( x , t ) = 1 N ∑ i : B i m = 1 C i l ( t ) = 1 δ ( x − x i ( t ) )
Empirical Distribution of Individuals Formulation
empirical distribution of individuals that follow a medium and influencer