Is a tilde or an equals sign correct in linear mixed model formulas? I know the formula for a linear mixed model (LMM) is often (always?) written with a tilde, rather than an equals sign, between the LHS and RHS. For example, one would write
outcome ~ 1 + var1 + (1|var2)
to denote that the outcome variable is modeled by an intercept plus var1 plus var2 with random effects (random intercept model).
I am doing proofs of a paper with LMM equations in the methods, and the journal for some reason has trouble rendering the tilde symbol properly (appears instead as a dash). So my questions is, is it also acceptable to write the formula with an equals sign instead of a tilde? Is there a difference, or would this be the incorrect way of writing a formula for a LMM?

The tilde as a relational operator is frequently used in a statistical context to indicate "is distributed as," and read "the term(s) on the left are distributed as indicated by the terms on the right." You will frequently see this indicating a simple distribution model, such as the "$\varepsilon \sim \mathcal{N}(0,\sigma^{2})$" in a regression context, indicating the errors are modeled with a normal distribution centered on zero and with variance $\sigma^{2}$. In a regression context you may also see an expectation of the dependent variable conditional on independent variables, or complex error structures expressed this way. (Aside: What you have written looks more like R code than mathematical notation in a textual context, and @AdamO makes a good point about deficiencies in this notation.)
By contrast the equals sign as a definitional operator is used to indicate just that: mathematical equality in a definitional sense; for example, in a regression context, you may define the way every observed value of a dependent variable is a function of both a fixed, or deterministic model, and a random, or stochastic model (the latter of which is often subsequently expressed with tilde notation to indicate distribution model, as in the snippet in the above paragraph). Sometimes a link function is left implicit in the mathematical formalism (e.g., where the text indicates something like "where the term to the left of the equals sign is the anti-link function of the dependent variable"), and sometimes it will be explicitly articulated in the mathematical formalism on either the left or right side of the equals sign.
