diff b1f9bc4..6fbd3ac trace_reconstruction_anchor_induction_v2.txt
diff --git a/trace_reconstruction_anchor_induction_v2.txt b/trace_reconstruction_anchor_induction_v2.txt
index 02f3af4..001daa8 100644
--- a/trace_reconstruction_anchor_induction_v2.txt
+++ b/trace_reconstruction_anchor_induction_v2.txt
@@ -172,7 +172,7 @@ finite partitions.
at radius r. We only use one consequence: a large value at one
interior point forces a comparable value somewhere on any arc that
carries enough Poisson weight. Boundary zeros are harmless; apply the
- inequality to log(|f| + delta) and let delta tend to 0.
+ ineuality to log(|f| + delta) and let delta tend to 0.
FACT 6 (Hadamard three-lines). If G is analytic and |G| <= 1 in the
vertical strip a <= Re s <= b, then log sup_{Re s = t} |G| is a
@@ -533,7 +533,7 @@ or none at all, in which case eta = 0; this gives the -eta z^u term.
Every further occurrence, in either string, ends at least P_0 away from
d, giving the tail.
-8.5 The pivot by the Poisson inequality.
+8.5 The pivot by the Poisson ineuality.
Let v = 10 log(P_0) / P_0. At the positive real point z = exp(-v):
@@ -556,7 +556,7 @@ On the circle |z| = exp(-a_0) the crude bound |H(z)| <= 2/a_0 holds.
There are at most about 1/a_0 contributing offsets, each coefficient at
most 2; since 1/a_0 is astronomically large, this is trivial.
-The Poisson inequality on the disk of radius exp(-a_0) centred at 0,
+The Poisson ineuality on the disk of radius exp(-a_0) centred at 0,
evaluated at the interior point exp(-v) which is much closer to 1, then
gives
@@ -709,7 +709,7 @@ and we define
G_cal = sum_l k_l g_l, Q = sum_l k_l q_l.
-The Poisson inequality, applied to the pivot bound on J_diamond, implies
+The Poisson ineuality, applied to the pivot bound on J_diamond, implies
the deficit budget
G_cal + Q <= 1.003.
@@ -792,7 +792,7 @@ Table. Round |v_0^*| up to w in {1,2,3,4,5}. Set
M .419 .357 .297 .246 .208
J_* .524 .453 .380 .335 .292
-These are conservative, in the sense of the four inequalities
+These are conservative, in the sense of the four ineualities
M < 1/2 - (2/pi) arctan( exp(-pi/S) ) - .0002
J_* < (1/pi)( arctan(S+w) + arctan(S-w) ) - .0002
@@ -1350,7 +1350,7 @@ actual traces.
<= |1 - u|^2/(1 - |u|^2) + |1 - v|^2/(1 - |v|^2). (14.3)
Proof: 1 - uv = (1 - u) + u(1 - v), then the weighted
- Cauchy-Schwarz inequality with weights (1 - |u|^2) and
+ Cauchy-Schwarz ineuality with weights (1 - |u|^2) and
|u|^2 (1 - |v|^2), whose sum is exactly 1 - |uv|^2.
Apply (14.3) with u = z_0, which has kappa >= 4/p, and v =
@@ -1477,7 +1477,7 @@ Fix x and y. Let delta = |E_x T - E_y T|. By Claim 14.2, T takes
values in [0,1] after the harmless shift T -> (T + 1)/2, which does not
change the gap.
-Hoeffding's inequality: with N independent traces, the empirical
+Hoeffding's ineuality: with N independent traces, the empirical
average of T deviates from its mean by delta/2 with probability at most
2 exp(-N delta^2/2). So
@@ -1634,7 +1634,7 @@ This extension concerns sample complexity only.
Fine and Wilf. "Uniqueness theorems for periodic functions." The
period lemma.
- Hoeffding. "Probability inequalities for sums of bounded random
+ Hoeffding. "Probability ineualities for sums of bounded random
variables." The concentration used in section 15.
Rubinstein. "Explicit separating words." The period and separation