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(bashref.info)Tilde Expansion

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Tilde Expansion
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   If a word begins with an unquoted tilde character (`~'), all of the
characters up to the first unquoted slash (or all characters, if there
is no unquoted slash) are considered a TILDE-PREFIX.  If none of the
characters in the tilde-prefix are quoted, the characters in the
tilde-prefix following the tilde are treated as a possible LOGIN NAME.
If this login name is the null string, the tilde is replaced with the
value of the `HOME' shell variable.  If `HOME' is unset, the home
directory of the user executing the shell is substituted instead.
Otherwise, the tilde-prefix is replaced with the home directory
associated with the specified login name.

   If the tilde-prefix is `~+', the value of the shell variable `PWD'
replaces the tilde-prefix.  If the tilde-prefix is `~-', the value of
the shell variable `OLDPWD', if it is set, is substituted.

   If the characters following the tilde in the tilde-prefix consist of
a number N, optionally prefixed by a `+' or a `-', the tilde-prefix is
replaced with the corresponding element from the directory stack, as it
would be displayed by the `dirs' builtin invoked with the characters
following tilde in the tilde-prefix as an argument (Note: The Directory
Stack).  If the tilde-prefix, sans the tilde, consists of a number
without a leading `+' or `-', `+' is assumed.

   If the login name is invalid, or the tilde expansion fails, the word
is left unchanged.

   Each variable assignment is checked for unquoted tilde-prefixes
immediately following a `:' or `='.  In these cases, tilde expansion is
also performed.  Consequently, one may use file names with tildes in
assignments to `PATH', `MAILPATH', and `CDPATH', and the shell assigns
the expanded value.

   The following table shows how Bash treats unquoted tilde-prefixes:

`~'
     The value of `$HOME'

`~/foo'
     `$HOME/foo'

`~fred/foo'
     The subdirectory `foo' of the home directory of the user `fred'

`~+/foo'
     `$PWD/foo'

`~-/foo'
     `${OLDPWD-'~-'}/foo'

`~N'
     The string that would be displayed by `dirs +N'

`~+N'
     The string that would be displayed by `dirs +N'

`~-N'
     The string that would be displayed by `dirs -N'